Capillarity Pressure Research Articles

Dual mechanisms of fiber dispersion of CF/Sn50Pb50 composites fabricated by double-layer printing head 3D printing process

Abstract Fiber dispersion was one of the crucial factors, which influenced the mechanical properties of fiber reinforced metal matrix composites (FR-MMCs). The incomprehension of fiber dispersion mechanisms and the lack of control methods limited the developments and further applications of the 3D printed FR-MMCs. In this work, the tensile properties and microstructures of continuous carbon fiber reinforced SnPb matrix composites, which were fabricated by the double-layer printing head 3D printing process (DPP), were measured and observed. The dual mechanisms of capillarity pressure driving and nonuniform interface reaction driving in fiber dispersion were proposed. Besides, the dynamic of fiber dispersion was discussed. It was found that improving wicking performance could increase the dispersion of fibers. This research filled in the blank of fiber dispersion mechanisms of 3D printed FR-MMCs, and provided the methodological supports for further improving the performances of composites.

Contribution of the capillary pressure second-order term on fast drying of cement-based materials

Standard models used to predict moisture transport of cement-based materials are based on quasi-static behaviour laws. However, it is not appropriate for fast drying condition. In this paper, a model taking into account dynamic effects on capillarity pressure is presented for the analysis of moisture transport in deforming cement-based materials. The proposed model is discretized in space by finite element method and in time by an implicit approximation-backward Euler method. On the basis of a drying experiment for cement paste, the dynamic model and non-dynamic model have been implemented and compared. Experimental data verifications indicate that dynamic model gives better results than static one. Moreover, the comparisons of numerical simulations reveal that dynamic capillarity effect has non-negligible influence on deformation and permeability. All investigations allow concluding that dynamic effects on capillary pressure should be taken into account to quantify moisture transport for fast drying condition.

Electric forces effect on field-assisted sintering

Electric forces acting on crystallographic defects generated at the flash onset or due to the surface polarization of the dielectric surrounding pores have been claimed to interact with the sintering kinetics upon flash processes. Herein, we estimated the magnitude of the external field-induced forces pointing out that the surface polarization does not play significant role on sintering. Moreover, the electric forces acting on charged defects are negligible when compared with the sintering stresses in the majority of flash experiments, only becoming comparable with the capillarity pressures when the external field is in the order of 103 V cm−1. Therefore, they can be of some relevance during flash sintering of resistive compounds like alumina or silicate glasses, they remaining normally not relevant otherwise.

“Digital Fluid Physics”: Prediction of phase equilibria for several mixtures of CO2 with petroleum fluid systems

Enhanced oil recovery (EOR) techniques (miscible/near miscible hydrocarbon/non-hydrocarbon gas injection, chemical flooding such as surfactant/polymer and smart water, and combinations of the three) aim at increasing oil recovery factor over what could be achieved from natural depletion and pressure maintenance methods such as waterflooding. As we embark on more complex EOR processes (e.g.), complex phase equilibria, complicated rock/fluid interaction, and sophisticated transport through porous media will create several key technical challenges that must be addressed.Currently, all of the existing compositional reservoir simulators, such as ECLIPSE, CMG, NEXUS, etc., use semi-empirical cubic equation of state (EoS) to represent the phase equilibria (mainly for the hydrocarbon calculation of equilibrium phase compositions) and phase properties (densities, viscosities, volume fractions, saturations, etc.). These data in combination with rock/fluid interaction data (relative permeability and capillarity pressure) will describe transport through porous media under the assumption of instantaneous equilibrium. Many empirical binary interaction parameters are needed for cubic EoS. In addition, mixing parameters along with the proper mixing rules are also required for multi-component mixtures. Current cubic EOS models have limited extrapolation capabilities beyond measured data. They also fall short in predicting derivative properties (even within the range measurements), transport properties, critical behavior, and the surfactants and polar components' phase behavior.This work presents the application of “Digital Fluid Physics” to determine the phase behavior of petroleum mixtures. Three different petroleum systems are investigated. Molecular simulation shows promising results in comparison with experimental measurements and therefore can reduce the cost and time required for tuning equations of state.

Fully mass-conservative IMPES schemes for incompressible two-phase flow in porous media

In this paper we consider fully mass-conservative numerical schemes for the simulation of incompressible and immiscible two-phase flow in porous media with capillary pressure. Compared with two kinds of conventional IMplicit Pressure Explicit Saturation (IMPES) schemes, the new schemes deserve a merit that the conservation of mass of both phases can be obtained. The total conservation equation is obtained by the summation of the discretized conservation equation for each phase. This approach is quite different from the conventional IMPES schemes. We present two kinds of fully mass-conservative IMPES schemes to solve the coupled systems for pressure, auxiliary velocity and saturation of each phase. The upwind mixed finite element methods are used to solve the pressure–velocity systems which can be decoupled, and the problems in the decoupled systems can be proved to be well-posed. Moreover, the new schemes are unbiased and the saturation of each phase can be proved to be bounds-preserving if the time step size is smaller than a certain value. The new schemes can also be applied to approximate the incompressible and immiscible two-phase flow in heterogeneous porous media with different capillarity pressures. Several interesting examples of incompressible and immiscible two-phase flow in porous media are presented to demonstrate the robustness of the new algorithms.

Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure

The Richards equation is a mathematical model for unsaturated flow through porous media. This paper considers an extension of the Richards equation, where non-equilibrium effects like hysteresis and dynamic capillarity are incorporated in the relationship that relates the water pressure and the saturation. The focus is on travelling wave solutions, for which the existence is investigated first for the model including hysteresis and subsequently for the model including dynamic capillarity effects. In particular, such solutions may have non monotonic profiles, which are ruled out when considering standard, equilibrium type models, but have been observed experimentally. The paper ends with numerical experiments confirming the theoretical results.

High temperature capillarity in hardmetal surface layers

A reason for the presence or absence of thin Co layers on a surface of WC–Co hardmetal articles after sintering has been a riddle for a long time. Such shiny Co layers are sometimes present on the surface of sintered WC–Co articles and their formation is referred to as “Co capping” in literature. Here we propose a detailed mechanism explaining the presence or absence of such thin cobalt layers on hardmetal articles after sintering. The proposed mechanism is based on considering wetting phenomena of WC by liquid Co in hardmetal surface layers and capillarity pressures acting on the liquid Co in narrow channels between WC grains in the surface layers. The mechanism explains all the phenomena of the Co layer formation during sintering of various hardmetal grades followed by either fast or slow cooling.

Modeling the effect of surface forces on the equilibrium liquid profile of a capillary meniscus.

The equilibrium profile of a capillary meniscus formed under combined action of disjoining/conjoining and capillarity pressures is investigated. Attention is focused on the shape of a transition zone between a spherical meniscus and a thin liquid film in front of the meniscus. The Poisson-Boltzmann equation is used for calculations of electrostatic contribution to the disjoining/conjoining pressure and the liquid shape inside the transition zone. Both complete and partial wetting conditions are investigated.

Large-scale Numerical Modelling of CO2 Injection and Containment Phases for an Italian Near-coast Reservoir Using PFLOTRAN

A potential CO2 storage site located offshore the west coast of Italy, has been modelled using PFLOTRAN assuming an injection rate of 1.5 Mtons/year for 20 years. The model predicts a CO2 footprint characterised by a diameter of about 3.5km and a maximum pressure build up of 38 bars. The solubility trapping has been quantified, predicting a dissolution in brine of 69% and 79% of the total amount of CO2 injected after 1000 and 2000 years respectively. The residual trapping has also been found to play an important role, with 9% and 6% of the injected CO2 being locked into the hosting matrix pores after 1000 and 2000 years respectively. Considering a worst-case scenario for leakages, where zero critical capillarity pressure has been assumed, minor CO2 leakages through the caprock have been identified, caused by the combined effects of the long-term structural trapping and the large and lasting overpressure caused by the CO2 injection in an ideally closed system. Finally, some preliminary work undertaken as part of an ongoing effort to couple a geochemical model to the multi-phase flow simulations reveals i) small changes in mineral volume fraction and porosity during and after the injection (∼5% after 1000 years), and ii) a not negligible self-sealing effect due to precipitation of calcite in the lower layer of the caprock. Further investigations and longer physical time runs are needed to confirm this assumption, but also to gain more confidence on the geochemical model built so far and to estimate the mineral trapping potential for this site.

A new treatment of capillarity to improve the stability of IMPES two-phase flow formulation

In this paper, we present an efficient numerical method for two-phase immiscible flow in porous media with different capillarity pressures. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressure functions. One popular scheme is to split the system into a pressure and a saturation equation, and to apply IMplicit Pressure Explicit Saturation (IMPES) approach for time stepping. One disadvantage of IMPES is instability resulting from the explicit treatment for capillary pressure. To improve stability, the capillary pressure is usually incorporated in the saturation equation which gradients of saturation appear. This approach, however, does not apply to the case of different capillary pressure functions for multiple rock-types, because of the discontinuity of saturation across rock interfaces. In this paper, we present a new treatment of capillary pressure, which appears implicitly in the pressure equation. Using an approximation of capillary function, we substitute the implicit saturation equation into the pressure equation. The coupled pressure equation will be solved implicitly and followed by the explicit saturation equation. Five numerical examples are provided to demonstrate the advantages of our approach. Comparison shows that our proposed method is more efficient and stable than the classical IMPES approach.

Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures

Contrast in capillary pressure of heterogeneous permeable media can have a significant effect on the flow path in two-phase immiscible flow. Very little work has appeared on the subject of capillary heterogeneity despite the fact that in certain cases it may be as important as permeability heterogeneity. The discontinuity in saturation as a result of capillary continuity, and in some cases capillary discontinuity may arise from contrast in capillary pressure functions in heterogeneous permeable media leading to complications in numerical modeling. There are also other challenges for accurate numerical modeling due to distorted unstructured grids because of the grid orientation and numerical dispersion effects. Limited attempts have been made in the literature to assess the accuracy of fluid flow modeling in heterogeneous permeable media with capillarity heterogeneity. The basic mixed finite element (MFE) framework is a superior method for accurate flux calculation in heterogeneous media in comparison to the conventional finite difference and finite volume approaches. However, a deficiency in the MFE from the direct use of fractional flow formulation has been recognized lately in application to flow in permeable media with capillary heterogeneity. In this work, we propose a new consistent formulation in 3D in which the total velocity is expressed in terms of the wetting-phase potential gradient and the capillary potential gradient. In our formulation, the coefficient of the wetting potential gradient is in terms of the total mobility which is smoother than the wetting mobility. We combine the MFE and discontinuous Galerkin (DG) methods to solve the pressure equation and the saturation equation, respectively. Our numerical model is verified with 1D analytical solutions in homogeneous and heterogeneous media. We also present 2D examples to demonstrate the significance of capillary heterogeneity in flow, and a 3D example to demonstrate the negligible effect of distorted meshes on the numerical solution in our proposed algorithm.

A degenerate parabolic system for three-phase flows in porous media

A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilin-ear parabolic system. A global existence theorem is proved under some hypotheses on the model data.

Non-local parabolic systems: applications in the three-phase capillary fluid filtration

Non-local degenerate parabolic systems arise in three-phase capillary flows in porous media under a pressure control at the inflow- and outflow-boundaries. A mathematical study of such systems is performed for a class of capillarity pressure functions corresponding to triangular capillarity-diffusion tensors. To this end a theory of non-degenerate parabolic approximations is developed: the unique global solvability of initial boundary-value problems is proved.

On the Influence of Boundary Conditions on Flows in Porous Media

Darcy’s law for a single phase flow in a porous medium states that k V p, where V is the fluid velocity, p is the fluid pressure, is the fluid viscosity, and k is the porous medium permeability. For two-phase flows, V k p , i 1, 2, where the relative permeabilities k now i i i i i depend on u and u , the saturations of both fluids. Since u u 1, we 1 2 1 2 Ž . Ž . may write u u and k k u , i 1, 2. Moreover, p p p u , 1 i i 1 2 c where the capillarity pressure p is a known function of u. A usual c Ž . procedure to determine the relative permeability curves k u is the i following. Water is injected at the inlet of the core, initially filled with oil, and the oil flux is measured at the outlet. Then the inverse problem of the Ž . permeability determination is hopefully solved. The two-phase evolution Ž . is modeled by the equation for the oil saturation u x, t ,

Recherches sur les mécanismes du concrétionnement. Coefficients d'activité des ions, solubilité des sels et de la silice dans les pores de petite taille

Variation of salt or silica solubility as a function of water activity, capillarity pressure or pore size, is discussed as a probable origine of matter migration, concentration, and finally concretioning.

Gravity and Capillarity Effects on Imbibition in Porous Media

Abstract This paper tries to assess the laboratory experiments used to scale gravity and capillarity-two active forces in the recovery process from matrix blocks in fissured reservoirs. We performed imbibition tests that show a great discrepancy among the scaled recovery curves corresponding to different block sizes. Several reasons tire considered to explain the failure of scaling rules:flow boundary conditions,local heterogeneities, andinstabilities in the water sweep. Introduction The numerical models used to forecast the behavior of fissured reservoirs now in service imply a knowledge of the particular recovery functions for matrix blocks. The aim is to provide the reservoir engineer with the simplest way w determine these recovery functions - by defining the conditions that must be respected so that laboratory tests on small samples may be used with scaling rules to simulate the behavior of a reservoir block. To keep the proper relationship between capillarity and gravity, Kyte suggested that gravity be artificially increased by carrying out the test in a centrifugal machine. This study tests the validity of this method. First we must examine from an analysis of the equations governing the problem, on which dimensionless groups (combinations of physical quantities) the recovery function of a block depends. Next, we must verify the theoretical conclusions of this analysis by experimenting on small-scale samples of a given shape and size, simulating the intensity of gravity by tests in a centrifugal machine. Then, we try to check the validity of scaling rules using cases in which experimental comparison can be achieved - imbibition experiments on samples geometrically similar, but of different sizes (diameters of 200, 70, and 40 mm). Results showed that these scaling rules were not valid. We then tried to isolate the phenomena that lead to the inadequacy of the conventional mathematical formulation by direct observation and by local measurement of saturation on the blocks during imbibition. THEORETICAL BASES Consider oil recovery from a cylindrical block of homogeneous, porous medium, initially saturated with oil and interstitial water, and then suddenly plunged into water. In the sample, the two plunged into water. In the sample, the two mechanisms of oil displacement by water (capillarity and gravity) are associated closely to contribute to production from a block, but their relative importance production from a block, but their relative importance depends on the dimensions of the block. Gravity becomes more important when the block is bigger, compared with capillarity. Theoretical study is based on the validity of the classical formulation of polyphasic flows in porous media on a macroscopic scale - that is, porous media on a macroscopic scale - that is, relative permeability and capillarity pressure. An analysis of the structure of the equations (Appendix) made it possible to reduce the parameters of the problem to a small number, such as problem to a small number, such as three dimensionless groups:(shape factor)(mobility ratio)(capillarity/gravity ratio)initial water saturationthe shape of the relative permeability curves and the reduced capillary pressure SPEJ P. 195