A Non-isothermal Pore Network Drying Model with Gravity Effect

The concept of immiscible displacement as an invasion percolation (IP) process driven by heat and mass transfer is used in a pore network model for convective drying of capillary porous media. The coupling between heat and mass transfer occurs at the liquid–gas interface through temperature-dependent equilibrium vapor pressure and surface tension as well as the phase change enthalpy (in evaporation and condensation). The interfacial effects due to capillary forces and gravity are combined in an invasion potential; viscous forces are neglected. Simulation results show stabilized invasion patterns and finite drying front width by the influence of gravity.     

A study of loop heat pipe with biporous wicks

The purpose of this study is to investigate the effects of various bimodal pore size distributions of biporous wicks for a loop heat pipe (LHP). The study was conducted following a statistical method using a two-level factorial plan involving three variables (particle size of pore former:74–88 and 125–149 μm Na₂CO₃, pore former content:20% by volume and 25% by volume, sintering temperature:700 and 750°C). Finally, the heat transport capability of the LHP between monoporous wicks and biporous wicks has been investigated. Experimental results show that, at the sink temperature of 10°C and the allowable evaporator temperature of 80°C, the heat transfer capacity of the better biporous wick achieved 200 W and the total thermal resistance was 0.31°C/W. The performance is enhanced about 60%, compared to a monoporous wick for 125 W and 0.53°C/W. Therefore, LHPs with biporous wicks are very attractive for high heat flux applications in the future.     

Towards a theory of nonequilibrium multiphase filtration flow

A new theoretical model of joint filtration flow of immiscible incompressible fluids is presented. This model takes into account relaxation processes due to the exchange of the fluids between pores of different sizes, and these relaxation processes are driven by capillary forces. The fluids occupy connected regions in the four-dimensional space formed by three coordinates and the pore length scale. When fluid exchange between pores of given sizes is effected by way of successive flow through pores of all intermediate sizes, the fluid pressure within each region is governed by a hyperbolic equation, the role of time being played by the pore linear scale. Pressure jumps across hypersurfaces separating these regions are equal to corresponding values of capillary pressure. A supplementary condition at any such hypersurface requires the speed of its displacement in the four-dimensional space to coincide with the normal velocity components of both the adjoining fluids. As a result, a new formulation of multiphase filtration flow problems is gained with allowance made for capillary relaxation in the porous space.     

Numerical simulation of the modulated flow pattern for vertical upflows by the phase separation concept

The multiphase heat transfer could be enhanced by creating thin liquid film on the wall. The phase separation concept is called due to the separated flow paths of liquid and gas over the tube cross section to yield thin liquid film. Our proposed heat transfer tube consists of an annular region close to the wall and a core region, interfaced by a suspending mesh cylinder in the tube. The heat transfer tube is a multiscale system with micron scale of mesh pores, miniature scale of annular region and macroscale of tube diameter and length. Great effort has been made to link from micron scale to macroscale. The Volume of Fluid (VOF) method simulates air/water two-phase flow for vertical upflow. The three-dimensional system was successfully converted to a two-dimensional one by using three equivalent criteria for mesh pores. The non-uniform base grid generation and dynamic grid adaption method capture the bubble interface. The numerical results successfully reproduce our experimental results. The numerical findings identify the following mechanisms for the enhanced heat transfer: (a) counter-current flow exists with upward flow in the annular region and downward flow in the core region; (b) void fractions are exact zero in the core region and higher in the annular region; (c) the liquid film thicknesses are decreased to 1/6–1/3 of those in the bare tube section; (d) the gas–liquid mixture travels much faster in the annular region than in the bare tube; (e) three-levels of liquid circulation exists: meter-scale bulk liquid circulation, moderate-scale liquid circulation around a single-elongated-ring-slug-bubble, and microliquid circulation following the ring-slug-bubble tails. These liquid circulations promote the fluid mixing over the whole tube length and within the radial direction. The modulated parameters of void fractions, velocities and liquid film thicknesses in the annular region and three-levels of liquid circulation are greatly beneficial for the multiphase heat transfer enhancement.     

Numerical Simulation of Porosity in Cements

The pores in cementitious materials, their sizes and connectivity have an important influence on the durability of concrete. Several microstructural models have been developed to simulate the three-dimensional pore network in cement pastes. In this article, microstructures with the $\upmu $ μ ic model are compared with experimental results. It is seen that despite having a resolution for the capillary pores very close to reality, the experimentally observed breakthrough diameter from mercury intrusion is much lower than the values obtained by applying an algorithm of mercury intrusion to the simulated microstructure. The effect of some of the most important input parameters on the pore sizes in the simulated microstructure explored. The phenomenon which seems best able to explain this discrepancy is that C–S–H is not in fact a phase with a smooth surface as represented in microstructural models, but a phase which grows as needles into the pore space, leading to very small water-filled capillary pores from quite young ages. The results demonstrate it will be extremely challenging to represent the porosity of real microstructures in microstructural models on the scale of hundreds of microns necessary to study macroscopic transport.     

Time-Dependent Diffusion and Surface-Enhanced Relaxation in Stochastic Replicas of Porous Rock

Understanding the connection between pore structure and NMR behavior of fluid-saturated porous rock is essential in interpreting the results of NMR measurements in the field or laboratory and in establishing correlations between NMR parameters and petrophysical properties. In this paper we use random-walk simulation to study NMR relaxation and time-dependent diffusion in 3D stochastic replicas of real porous media. The microstructures are generated using low-order statistical information (porosity, void–void autocorrelation function) obtained from 2D images of thepore space. Pore size distributions obtained directly by a 3D pore space partitioning method and indirectly by inversion of NMR relaxation data are compared for the first time. For surface relaxation conditions typical of reservoir rock, diffusional coupling between pores of different size is observed to cause considerable deviations between the two distributions. Nevertheless, the pore space correlation length and the size of surface asperity are mirrored in the NMR relaxation data for the media studied. This observation is used to explain the performance of NMR-based permeability correlations. Additionally, the early time behavior of the time-dependent diffusion coefficient is shown to reflect the average pore surface-to-volume ratio. For sufficiently high values of the self-diffusion coefficient, the tortuosity of the pore space is also recovered from the long-time behavior of the time-dependent diffusion coefficient, even in the presence of surface relaxation. Finally, the simulations expose key limitations of the stochastic reconstruction method, and allow suggestions for future development to be made.     

Visualization of pool boiling on enhanced surfaces

This work reports experiments to visualize nucleate boiling on an enhanced tubular surface having sub-surface tunnels and surface pores. The finned copper tube had 1575 fins/m (40 fins/in.) and 0.8 mm fin height. The fins are covered by a thin foil sheet having 0.23 mm pores at 1.5 mm pore pitch along each interfin region. Data are provided for two foil cover sheets, one copper and the other a transparent plastic. The uniqueness of this work is that the visualization method allowed direct observation of the boiling process in the subsurface tunnels. Use of a high speed camera with 30 × magnification allowed detailed observation of the evaporation process in the tunnels and of the vapor bubbles emerging from the pores. The experiments were conducted for saturated and subcooled boiling in the horizontal and vertical orientations. For the vertical tube, the saturated boiling experiments showed that all of the tunnels were vapor filled except for liquid menisci in the corners. This was also true for the horizontal tube at high heat flux. For the horizontal tube at low heat flux, portions of the tunnel length was liquid filled. A large portion (70–90%) of the region was vapor filled except for liquid menisci in the corners, and the remaining part of the region had oscillating menisci. These experiments provide conclusive proof that the heat transfer mechanism in the subsurface tunnels is evaporation on the menisci in the corners.     

Investigation of thermocapillary convective patterns and their role in the enhancement of evaporation from pores

The present work investigates the evaporation process from a liquid meniscus formed in capillary tubes of various sizes. A very strong convection within the liquid phase is observed; it is proposed that the non-uniform evaporation from the meniscus leads to a temperature gradient along the interface causing a surface tension gradient, which is the driving mechanism for the convection. The observed convection is shown to be clearly correlated to the evaporation rate and the volatility of the liquid. Unlike Marangoni convection observed by imposing a temperature gradient, this is a self-induced driving gradient caused by evaporative cooling effect.The Marangoni roll in the liquid phase has been visualized and characterized using seeding particles. It is shown in the present study that the observed convection contribute in enhancing the heat–mass transfer from the pore. The experimental results show that when the meniscus recedes inside the pore, the convection slows down and eventually stops. A theoretical model is developed to describe the temperature gradient, which establishes due to the evaporative cooling effect between the centre and the wedge of the meniscus. The results of the model show a good qualitative agreement with the experimental observations.     

Pore Scale Modeling of Rate Effects in Imbibition

We use pore scale network modeling to study the effects of flow rate and contact angle on imbibition relative permeabilities. The model accounts for flow in wetting layers that occupy roughness or crevices in the pore space. Viscous forces are accounted for by solving for the wetting phase pressure and assuming a fixed conductance in wetting layers. Three-dimensional simulations model granular media, whereas two-dimensional runs represent fracture flow.We identify five generic types of displacement pattern as we vary capillary number, contact angle, and initial wetting phase saturation: flat frontal advance, dendritic frontal advance, bond percolation, compact cluster growth, and ramified cluster growth. Using phase diagrams we quantify the range of physical properties under which each regime is observed. The work explains apparently inconsistent experimental measurements of relative permeability in granular media and fractures.     

Wärmeübergang mit Phasenumwandlung bei Fallfilmen

In these papers the heat transfer in thin liquid films with low evaporation and extensive one will be studied. First the knowledge of thin films without heat transfer serves to build up new theories to calculate Nusselt numbers for heat transfer at low evaporation. These resulted formulaes are extended to not negligible heat transfer rates. The results are parameters, which are characteristic for extensive heat transfer rates. The influence of these new calculated parameters will be expected and compared with experimental datas.

     

Simulation of the dynamic (frequency-dependent) permeability and electrical conductivity in porous materials based on the concept of an ensemble of pores

The class of models of porous media based on the concept of an ensemble of pores with a certain distribution of the main geometrical parameters (e.g., pore size) is studied. The case of the saturation of the pore space with a single-phase multicomponent fluid mixture is studied with and without taking into account the transfer of electric charges. Transfer laws are derived from the condition of decreasing free energy. The hydrodynamic connectivity of pores (and electrical conductivity) is described by two kernels: one kernel describes the connectivity of pores in space, and the other describes the connectivity of pores in the elementary macrovolume. The frequency dependences of the dynamic permeability determined in laboratory experiments and the electrical conductivity of the porous medium were determined using the concept of an ensemble of pores. The relationship between the models considered and relaxation filtration models is established.     

Pore-Scale Imaging and Analysis of Wettability Order,Trapping and Displacement in Three-Phase Flow in Porous Media with Various Wettabilities

Three-phase flow in porous media is encountered in many applications including subsurface carbon dioxide storage, enhanced oil recovery, groundwater remediation and the design of microfluidic devices. However, the pore-scale physics that controls three-phase flow under capillary dominated conditions is still not fully understood. Recent advances in three-dimensional pore-scale imaging have provided new insights into three-phase flow. Based on these findings, this paper describes the key pore-scale processes that control flow and trapping in a three-phase system, namely wettability order, spreading and wetting layers, and double/multiple displacement events. We show that in a porous medium containing water, oil and gas, the behaviour is controlled by wettability, which can either be water-wet, weakly oil-wet or strongly oil-wet, and by gas–oil miscibility. We provide evidence that, for the same wettability state, the three-phase pore-scale events are different under near-miscible conditions—where the gas–oil interfacial tension is ≤?1 mN/m—compared to immiscible conditions. In a water-wet system, at immiscible conditions, water is the most-wetting phase residing in the corners of the pore space, gas is the most non-wetting phase occupying the centres, while oil is the intermediate-wet phase spreading in layers sandwiched between water and gas. This fluid configuration allows for double capillary trapping, which can result in more gas trapping than for two-phase flow. At near-miscible conditions, oil and gas appear to become neutrally wetting to each other, preventing oil from spreading in layers; instead, gas and oil compete to occupy the centre of the larger pores, while water remains connected in wetting layers in the corners. This allows for the rapid production of oil since it is no longer confined to movement in thin layers. In a weakly oil-wet system, at immiscible conditions, the wettability order is oil–water–gas, from most to least wetting, promoting capillary trapping of gas in the pore centres by oil and water during water-alternating-gas injection. This wettability order is altered under near-miscible conditions as gas becomes the intermediate-wet phase, spreading in layers between water in the centres and oil in the corners. This fluid configuration allows for a high oil recovery factor while restricting gas flow in the reservoir. Moreover, we show evidence of the predicted, but hitherto not reported, wettability order in strongly oil-wet systems at immiscible conditions, oil–gas–water, from most to least wetting. At these conditions, gas progresses through the pore space in disconnected clusters by double and multiple displacements; therefore, the injection of large amounts of water to disconnect the gas phase is unnecessary. We place the analysis in a practical context by discussing implications for carbon dioxide storage combined with enhanced oil recovery before suggesting topics for future work.

     

Predictive Pore-Scale Modeling of Single and Multiphase Flow

We show how to predict flow properties for a variety of rocks using pore-scale modeling with geologically realistic networks. The pore space is represented by a topologically disordered lattice of pores connected by throats that have angular cross-sections. We successfully predict single-phase non-Newtonian rheology, and two and three-phase relative permeability for water-wet media. The pore size distribution of the network can be tuned to match capillary pressure data when a network representation of the system of interest is unavailable. The aim of this work is not simply to match experiments, but to use easily acquired data to estimate difficult to measure properties and to predict trends in data for different rock types or displacement sequences.     

Statistical Synthesis of Imaging and Porosimetry Data for the Characterization of Microstructure and Transport Properties of Sandstones

The microstructure of a suite of sandstone samples is quantitatively analyzed using a method which combines information from thin section micrographs of the pore space with mercury injection porosimetry in a statistical framework. This method enables the determination of a continuous distribution of pore sizes ranging from few nanometre to several hundred micrometre. The data obtained unify fractal and Euclidean aspects of the void space geometry, yield estimates of the pore-to-throat aspect ratio and challenge the ability of commonly used network models to describe fluid percolation in multiscale porous media. Application of critical path analysis to the prediction of flow permeability and electrical conductivity of sandstone core samples using the new information produces results comparable to those obtained by the classical approach—a fact attributed to the presence of macroscopic heterogeneity at the scale of several millimetres.     

Modeling of isothermal processes in porous materials on the basis of the concept of an ensemble of pores

A class of models of porous media based on the concept of an ensemble of pores with a certain distribution of the main geometric parameters (for example, the pore size) is considered. The cases of pores saturated with single-and two-phase multicomponent liquid mixtures are investigated. The properties of equilibrium states of the mixture are derived from the minimum free energy condition and the transfer laws from the decreasing free energy condition. The hydrodynamic connectivity of the pores is described by two types of kernels: one describes the spatial connectivity and the other the connectivity in an elementary macrovolume. Analytically and numerically, the one-dimensional problems of establishment of a steady-state regime, propagation of a passive admixture, and two-phase flow (an analog of the Buckley-Leverett problem) are investigated. A relationship between the models in question and relaxational filtration models is demonstrated. A simple model of capillary hysteresis related with the non-monotonicity of the pore area to volume ratio function is proposed.     

Evaporation of Falling and Shear-Driven Thin Films on Smooth and Grooved Surfaces

One of the most important tasks in development of modern gas turbine combustors is the reduction of NO_x emissions. An effective way to reduce the NO_x emission is using the lean premixed prevaporization (LPP) concept. An important phenomenon taking place in LPP chambers is the evaporation of thin fuel films. To increase the fuel evaporation rate, the use of microstructured walls has been suggested. The wall microstructures make use of the capillary forces to evenly distribute the liquid fuel over the wall, so that the appearance of uncontrolled dry patches can be avoided. Moreover, the wall structures promote the thin film evaporation characterized by ultra-high evaporation rates. An experimental setup was built for the investigation of thin liquid films falling down on the outer surface of vertical tubes with either a smooth or structured surface. In the first testing phase water is used, fuel like liquids will be used later on. The thin film can be heated from both sides, by hot oil flowing inside the tube, and by hot compressed air flowing in co-current direction to the thin film. The film is partly evaporated along the flow. Results for the wavy film structure at different Reynolds numbers are reported. For theoretical investigations a model describing the hydrodynamics and heat transfer due to evaporation of the gravity- and shear-driven undisturbed liquid film on structured surfaces was developed. For low Reynolds numbers or low liquid mass fluxes the wall surface is only partly covered with liquid and the heat transfer is shown to be governed by the evaporation of the ultra-thin film in the vicinity of the three-phase contact line. A numerical model for the solution of a two-dimensional free-surface flow of a liquid film over a structured wall was also developed. The Navier–Stokes equations are solved using the Volume of Fluid (VOF) technique. The energy equation is included in the model. The model is verified by comparison with data from the literature showing favorable agreement. In particular, the proposed model predicts the formation of capillary waves observed in the experiments. The model is used to investigate the flow of liquid on a structured wall. This calculation is the first step towards the modeling of a three-dimensional wavy flow of a gravity- and shear-driven film along a wall with longitudinal grooves. It is found that due to the Marangoni effect, a circulating flow arises within the cavity, thereby leading to an enhancement in the evaporation rate.     

Investigation on Heat and Mass Transfer in a Evaporator of a Capillary-Pumped Loop with the Lattice Boltzmann Method: Pore Scale Simulation

A two-dimensional transient numerical model based on the lattice Boltzmann method (LBM) for the global evaporator of a capillary-pumped loop (CPL) is proposed to describe heat and mass transfer with evaporation in the porous wick, heat conduction in the cover plate, and heat transfer in the vapor groove. To indicate the stochastic phase distribution characteristics of most porous wick, the quartet structure generation set (QSGS) is introduced for generating more realistic microstructures of porous media. By using the present lattice Boltzmann algorithm along with the porous structure, the heat and mass transfer of an evaporator on pore scale can be predicted without resorting to any empirical parameters determined case by case. The energy equations for entire evaporator are solved as a conjugate problem, which are solved by means of a spatially varying relaxation time in the lattice Boltzmann model and the liquid flow is driven via the interfacial mass flux. A convective boundary condition considering the latent heat during the evaporation on the interface is introduced into the lattice Boltzmann model based on the nonequilibrium extrapolation rule. Especially, the bounce-back rule and the equilibrium rule of the LBM are, respectively, introduced to deal with the momentum boundary conditions inside the porous wick and on the evaporation interface in order to ensure the stability and the efficiency of the LBM model. Numerical results corresponding to different working conditions and different working fluids are presented, which provide guidance for the evaporator design of a CPL system.     

Influence of the structure of a porous medium on the residual gas saturation in the case of capillary displacement by a liquid

A model of a porous medium consisting of randomly branching conical pores is used to investigate the quasistatic displacement of gas by a wetting liquid without application of an external pressure. Allowance is made for the circumstance that in the capillary process all the pores have at least one-sided permeability for the liquid phase. An expression is obtained that relates the residual gas saturation to the parameters which characterize the structure of the pores and the wetting properties of the system. Two new characteristics of the pore space are introduced — the branching parameter and the opening angle of the pores — and the influence of these parameters on the residual saturation is investigated. It is shown that for individual classes of natural media the residual gas saturation depends only on the porosity and the contact angle of wetting.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 128–133, September–October, 1981.