Pore network simulation of fluid imbibition into paper during coating: II. Characterization of paper's morphology and computation of its effective permeability tensor

We describe a method for characterization of the microstructure of a paper, in terms of the statistical distribution of the effective radii and lengths of the channels between the paper's fibers, and the average coordination numbers that characterize the connectivity of such channels, both in the main planes of the paper and in the transverse direction perpendicular to these planes. The microstructure of the paper is then represented by a three-dimensional network of interconnected flow channels between the fibers. The geometrical characteristics of the channels, such as their effective radii and lengths, are selected from the statistical distributions obtained by the characterization method, as are the two average coordination numbers. Extensive computer simulations are carried out to compute the effective permeability tensor of the paper, and to investigate the effect of the various microstructural parameters on the tensor. These simulations indicate that the two average coordination numbers, as well as the spatial distribution of the fibers and their length, strongly influence the flow properties of a paper.     

Two-phase flow in porous media

Two-phase flow in porous media depends on many factors, such as displacement vs steady two-phase flow, saturation, wettability conditions, wetting fluid vs non-wetting fluid is displacing, the capillary number, interfacial tension, viscosity ratio, pressure gradient, uniformly wetted vs mixed-wet pore surface, uniform vs distributed pore throats, small vs large pores, well-connected pores vs pores connected by small throats, etc. These parameters determine how the two fluids are distributed in the pores, e.g. whether they flow in seperate channels or side-by-side in the same channels, either with both fluids being continous or only one fluid being continous and the other discontinuous. In displacement, the capillary number and the viscosity ratio determine whether the displacement front is sharp, or if there is either capillary or viscous fingering.     

Determination of the effects of the pore size distribution and pore connectivity distribution on the pore tortuosity and diffusive transport in model porous networks

An efficient computation method to study flow and transport process of small molecules in porous media using a dual site-bond lattice model, DBSM, is described. The microscopic properties of the porous network take into account the influence of local heterogeneities during the simulations. The numerical experiments demonstrated the combined effect of pore size distribution and connectivity distribution on the mass transport properties and the structural tortuosity. The results indicate that the pore size distribution and percolation phenomena related with pore shielding effects, influence significantly the tortuosity and the effective diffusivity of the porous network. Also, the simulations raise the important role of the connectivity distribution among the various pores in the gas diffusive properties of the poorly connected networks.     

富油煤（长焰煤）孔隙结构三维表征及渗流模拟

采用X射线CT(computed tomography)成像仪对富油煤(长焰煤)进行了三维表征,建立了统计孔径分布(PSD)的等效孔隙网络模型(PNM),研究了压力梯度和流动方向对渗流过程的影响。结果表明：孔隙、矿物和基质分别占总体积的11.30%、1.03%和87.67%,连通孔隙率为5.13%。孔隙等效半径在3~8 μm内的数量占89.23%,平均配位数为2.87,孔隙连通性较差。等效半径小于2 μm的喉道数占73%,喉道的等效长度主要分布在10~30 μm之间。在相同压力梯度下,三个方向的孔隙压力、渗流速度和流动路径分布不同,表现出各向异性。随着压力梯度的增大,渗流速度逐渐增大,且渗流速度随压力的变化呈现明显的非线性关系。三个方向上的调和平均渗透率为0.1403 mD,这与前人测得的榆神府矿区富油煤渗透率(0.1345 mD)相差在5%以内。     

A method to calculate the multiphase flow properties of heterogeneous porous media by using network simulations

A method is suggested to compute the capillary pressure and relative permeability curves of heterogeneous porous media. The broad pore radius distribution (PRD) and throat radius distribution (TRD) are decomposed into relatively narrow component distribution functions which are used for the computer‐aided construction of pore‐and‐throat networks. The quasi‐static motion of menisci in pores and throats is tracked by accounting for capillary forces. The presence of fractal roughness along pore walls ensures the coexistence of both phases in pores. The calculation of the hydraulic conductance of each phase is based on the concept of constricted unit cell. Simulations in component pore networks constructed from narrow PRD and TRD produce a set of capillary pressure and relative permeability functions, the arithmetic averaging of which yields the corresponding functions for a heterogeneous synthetic pore network. This information is used by a dynamic simulator of drainage in permeability networks to predict experimental results of soil columns. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Pore Network Drying Model for Particle Aggregates: Assessment by X-Ray Microtomography

Convective drying of disordered glass bead packings has been investigated both experimentally and numerically. X-ray microtomography (XMT) and image analysis techniques have been used to determine the three-dimensional spatial distribution of the liquid and solid phases at the pore scale within the wet particle aggregates. The evolution of the liquid distribution in the aggregate has been tracked during the drying process. Particle center coordinates and radii have been extracted from the X-ray images using binarization and segmentation techniques. Based on this geometric data for a real aggregate, a pore network approximation of the pore space has been generated from a Voronoi tessellation about particle centers by designating Voronoi edges as interconnected cylindrical pores with radii computed from the distance between neighboring particles. This three-dimensional irregular pore network takes into account both the geometrical and topological characteristics (pore size distribution and connectivity) of the actual pore space. Drying simulations have been carried out for the pore networks obtained from the XMT and results are presented as phase distributions and moisture profiles. The simulated liquid phase distributions are in qualitative agreement with the experimental result, which indicates that pore network models are suited to describe the drying of dense particle aggregates at the pore scale.     

Development of high efficiency particulate absorbing filter materials

We have developed new high efficiency particulate absorbing filter materials by bonding the fiber web with the help of high pressure water jets emerging from micron sized nozzles and subsequently coating the filters with a chemical binder. Two different types of nonwoven filters are produced by varying the water jet pressure during the bonding process. The performance characteristics of the filter materials are evaluated in terms of filtration parameters, such as filtration efficiency, dust holding capacity, and pressure drop. Filtration efficiency depends on the pore characteristics, namely pore size and their distribution in the filters. The developed filter materials have shown promising performance characteristics by capturing higher amount of dust particles with a relatively low pressure drop during use. These filter materials can be used for a wide range of industrial applications, where high filtration efficiency is required at low energy consumption. A fluid flow simulation is carried out by computational fluid dynamics (CFD) to understand flow pattern during the bonding process. The CFD is also used to predict the pressure drop in the nonwoven filter materials during filtration process. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Simulation of nitrogen adsorption-desorption isotherms. Hysteresis as an effect of pore connectivity

The sorption mechanisms in porous materials have been of long standing interest and debate. Concretely, the involved hysteresis during nitrogen adsorption-desorption processes and its interpretation has represented an important challenge for experimentalists and theoreticians. Moreover, a better understanding of the different observed hysteretic behaviors and the elapsed are as is still remaining. Such a scenario has motivated us to study the pore connectivity and pore size distribution effects upon the hysteresis in nitrogen adsorption-desorption isotherms of a porous solid. Our simulation has been carried out over the entire range of connectivity assuming three-dimensional pores randomly inscribed in a two-dimensional lattice with different occupation probabilities, related with pore connectivity, including the percolation threshold. The adsorption and desorption curves as a function of pressure have been simulated taking into account the monolayer-multilayer formation process and the capillary condensation-evaporation phenomena by using the Broekhoff de Boer and Kelvin equations, respectively. Results show that the employed methodology allows reproducing different types of hysteresis experimentally observed where the hysteretic behavior is strongly dependent upon both connectivity and the broadening of the pore size distribution. Specifically, the hysteresis loop area exhibits a maximum at the percolation threshold and then it decreases monotonically above the threshold.     

A novel simulation approach for particulate flows during filtration

This paper presents a novel approach for simulation of filtration process when velocity gradient within pore space cannot be neglected. The new model is useful for accurate prediction of the filtration performance and particle retention efficiency. Artificial porous media such as filters, by design, have a large surface-to-volume ratio because of an inherent homogeneity present within their structure; the homogenous structure is realized due to organized packing of grains as building blocks, which leads to a significant velocity gradient inner pore space. In this work, the inner-pore flow characteristics of two different homogeneous packing patterns (cubic and oblique hexagonal packing) were examined. The multiple constricted tubes analogy was adopted to model porous media to simplify the inner-pore geometrical structure. A new integrated simulation approach was utilized through implementing the particle trajectory model to every unit bed element of the simulation domain. The accuracy of the numerical simulations used in this study was verified by comparing the particle distribution pattern and penetration depth obtained from simulations to those monitored via a visual experiment. A sensitivity analysis was carried out to study parameters that may affect the particle distribution and penetration length, such as grain-to-particle size ratio, flow rate, and fluid viscosity. The simulation method utilized in this paper provides an in-depth understanding of the fine particle migration during filtration process through artificial porous media, and, thus, provide useful insights for improved filtration design.     

Pore-network analysis of two-phase water transport in gas diffusion layers of polymer electrolyte membrane fuel cells

A pore-network model was developed to study the water transport in hydrophobic gas diffusion layers (GDLs) of polymer electrolyte membrane fuel cells (PEMFCs). The pore structure of GDL materials was modeled as a regular cubic network of pores connected by throats. The governing equations for the two-phase flow in the pore-network were obtained by considering the capillary pressure in the pores, and the entry pressure and viscous pressure drop through the throats. Numerical results showed that the saturation distribution in GDLs maintained a concave shape, indicating the water transport in GDLs was strongly influenced by capillary processes. Parametric studies were also conducted to examine the effects of several geometrical and capillary properties of GDLs on the water transport behavior and the saturation distribution. The proper inlet boundary condition for the liquid water entering GDLs was discussed along with its effects on the saturation distribution.     

Visualizing multiphase flow and trapped fluid configurations in a model three‐dimensional porous medium

We report an approach to fully visualize the flow of two immiscible fluids through a model three‐dimensional (3‐D) porous medium at pore‐scale resolution. Using confocal microscopy, we directly image the drainage of the medium by the nonwetting oil and subsequent imbibition by the wetting fluid. During imbibition, the wetting fluid pinches off threads of oil in the narrow crevices of the medium, forming disconnected oil ganglia. Some of these ganglia remain trapped within the medium. By resolving the full 3‐D structure of the trapped ganglia, we show that the typical ganglion size, as well as the total amount of residual oil, decreases as the capillary number Ca increases; this behavior reflects the competition between the viscous pressure in the wetting fluid and the capillary pressure required to force oil through the pores of the medium. This work thus shows how pore‐scale fluid dynamics influence the trapped fluid configurations in multiphase flow through 3‐D porous media. © 2013 American Institute of Chemical Engineers AIChE J, 59:1022‐1029, 2013     

Pore network model of deactivation of immobilized glucose isomerase in packed-bed reactors. Part III: Multiscale modelling

A widely used method for converting glucose to fructose is by enzymatic isomerization. This process, which uses immobilized glucose isomerase, takes place in a packed-bed reactor that consists of microporous particles with a range of pore sizes, characterized by a pore size distribution. The micropores are also interconnected, giving rise to a three-dimensional (3D) network of pores with distributed sizes and connectivities. The particles themselves generate a 3D pore network at the reactor level with distributed pore sizes, but with a fixed connectivity. In this paper, Part III of a series, we develop a multiscale modelling approach to this problem, beginning with the relevant phenomena at the scale of the micropores, and integrating them into the particle and reactor length scales. As the efficiency of the process is significantly affected by deactivation of the microporous particles, we take this phenomenon into account at all the relevant length scales. We use a real random packing of particles, originally constructed by Finney (Proc. R. Soc. Lond. A, 319 (1970) 479), and map its pore space onto an equivalent 3D Voronoi network in which the pores are represented by the edges of the Voronoi polyhedra. The flow field in the Voronoi network is determined, and the convection-diffusion-reaction equation is then solved in the Voronoi network, taking into account the gradual deactivation of the microporous particles. Several plausible mechanisms of deactivation of the microporous particles are considered, and their effect on the performance of the reactor is investigated. Good agreement is found between the results of the computer simulations and the relevant experimental data.     

碳酸盐岩复杂结构储层流体识别方法研究

针对西部T油田以裂缝-孔隙类型为主的碳酸盐岩复杂储层特点,采用双重孔隙结构体积模型,以常规测井资料为基础求取储层内各孔隙度参数,应用基于统计分析的正态分布法对碳酸盐岩储层流体性质进行识别。通过对T油田两个区块二十余口井的应用及试油验证,认为该方法的地质效果良好。     

Three-dimensional pore network model of biofilter treating toluene: A study of the effect of the pore space morphology

Treatment of polluted air stream with toluene in a biofilter under quasi-steady-state condition is described with a three-dimensional (3-D) pore network model. The efficiency of the process depends on the pore structure of the biofilter media. The previous models for the process, considered transport and reaction equations mostly in the continuum systems. They cannot show the effect of pore spaces’ morphology, different pore size distributions and connectivity types. We used the 3-D pore network model to simulate the pore structure and to study the effects of biofilm growth on pore size distribution and pore connectivity on the biofilter performance. This model predicts the toluene conversion, pressure drop profiles, biofilm thickness and clogging in the biofilter. Our developed model assumes a nonlinear kinetic for the biodegradation reaction of toluene in the biofilm. The differential equations of the model are solved numerically. Model results indicated that biofilter media with smaller mean pore size and higher connectivity have a higher toluene conversion. To investigate the validity of the model, we compared the model results with experimental data and found satisfying similarities.     

非均质多孔盐水层中超临界CO_2的注入压力与饱和度分布特性

为了研究盐水层孔隙结构特性对CO2注入过程的影响,采用对数正态分布的随机分布孔隙率表征地下盐水层的非均质孔隙特性,引入与盐水层中局部温度和局部压力相适应的CO2密度和黏度,建立了超临界CO2-盐水体系的两相流驱替过程数学模型。通过数值模拟研究了超临界CO2注入的过程参数和盐水层特性对CO2注入特性和盐水层中饱和度分布的影响。研究表明:CO2的注入压力主要与盐水层的深度和盐水层的体积平均孔隙率有关,而受盐水层孔隙率分布的影响较小;盐水层的孔隙率分布特性对CO2饱和度分布影响非常显著;在盐水层总容积相同的条件下,深层盐水层的CO2存储容量比浅层盐水层的小,且注入压力大;在CO2封存过程中,应选择合适的注入速率,最大限度地提高盐水层封存容量的利用率。本文的计算方法和分析结果为超临界CO2的地下封存过程和注入后的评估方法等提供了计算方法和理论依据。     

Dynamic modeling of drainage through three-dimensional porous materials

The interplay of viscous, gravity and capillary forces determines the flow behavior of two or more phases through porous materials. In this study, a rule-based dynamic network model is developed to simulate two-phase flow in three-dimensional porous media. A cubic network analog of porous medium is used with cubic bodies and square cross-section throats. The rules for phase movement and redistribution are devised to honor the imbibition and drainage physics at pore scale. These rules are based on the pressure field within the porous medium that is solved for by applying mass conservation at each node. The pressure field governs the movement and flow rates of the fluids within the porous medium. Film flow has been incorporated in a novel way. A pseudo-percolation model is proposed for low but non-zero capillary number (ratio of viscous to capillary forces). The model is used to study primary drainage with constant inlet flow rate and constant inlet pressure boundary conditions. Non-wetting phase front dynamics, apparent wetting residuals (S_wr), and relative permeability are computed as a function of capillary number (N_ca), viscosity ratio (M), and pore-throat size distribution. The simulation results are compared with experimental results from the literature. Depending upon the flow rate and viscosity ratio, the displacement front shows three distinct flow patterns—stable, viscous fingering and capillary fingering. Capillary desaturation curves (S_wr vs. N_ca) depend on the viscosity ratio. It is shown that at high flow rates (or high N_ca), relative permeability assumes a linear dependence upon saturation. Pseudo-static capillary pressure curve is also estimated (by using an invasion percolation model) and is compared with the dynamic capillary pressure obtained from the model.     

Scale-up of pore-level relative permeability from micro- to macro-scale

Scaling up relative permeability curves of wetting and nonwetting phase of drainage and imbibition processes from pore scale to macro scale is a challenge. A new method for scaling up relative permeability from micro- to macro-scale is proposed based on electrical analogy of multiphase fluid flow at pore scale. The method is validated against four synthetic porous media generated using homogeneous and heterogeneous grain size distributions, each of which were cut into eight sub-segments. Single-phase and two-phase flow properties were calculated for the main blocks and the subsequent sub-segments using random network modelling technique. Then, the subsegments were randomly distributed in space to reconstruct the main blocks and the proposed scale-up method was employed to calculate the relative permeability curves of the reconstructed blocks. Results were compared to the ones obtained directly from the network model of the original blocks and show good agreement between the calculated and scaled-up relative permeability curves of primary drainage and secondary imbibition. Furthermore, the model was tested on real media. Eight network models were extracted from pore size distribution of core samples obtained from the Green River basin located in the Mesaverde Formation. Flow properties obtained from the network models were validated against experimental data and good agreement was observed. These network models show a higher level of heterogeneity at micro-scale. Then, the scale-up methods were employed in order to reconstruct the macro-scale sample and predict its properties. Scale-up methods successfully predict the single-phase and two-phase flow properties of the sample.     

Nonisothermal analysis of a couple stress fluid in blade coating process

In this paper, a nonisothermal analysis for the process of blade coating of an incompressible couple stress fluid is presented using both plane and exponential coaters. The governing system is simplified using lubrication approximation theory (LAT). The interesting quantities from engineering point of view like normalized pressure, maximum pressure, pressure gradient, velocity, and effects of involved parameters on temperature distribution, which influence the coating process are evaluated. It is observed that pressure is at maximum near the edge of the blade whereas fluid velocity and temperature are at maximum near the substrate. An increasing couple stress parameter increases the load and decreases the coating thickness. It is worth mentioning that load and pressure are the most significant outcomes of the present exertion as these two physical quantities ensure thickness and the quality of coating.     

Mercury porosimetry and the interpretation of pore geometry in sedimentary rocks and artificial models

The major objectives of this paper are to investigate how the form and hysteresis of mercury injection, withdrawal and reinjection capillary pressure curves are affected by the geometry of pores and their connections in samples of sedimentary rocks and also in artificial and theoretical pore-network models.In particular, those aspects of pore systems which may influence trapping of mercury during pressure reduction and withdrawal are considered. These are: pore to throat ratio, throat to pore coordination number or connectivity and the types and extent of random and non-random heterogeneities within the system.These aspects of pore systems influence the threshold pressure and the gradient of injection curves as well as the gradients and degree of hysteresis displayed by withdrawal and re-injection curves. Such curves are useful in interpreting pore geometry and give information which is valuable in assessing multiphase fluid behaviour in oil and gas reservoir rocks. In the case of water displacing oil or gas, in a strongly water-wet system, the trapping of oil or gas is controlled mainly by capillary forces and a direct analogy with the air-mercury system is possible.     

Coating and Drying in Spouted Bed: Influence of the Liquid-Particle Work of Adhesion

The aim of this work is to analyze the resulting process: coating or drying, and the respective fluid dynamic behavior, by bottom-spraying polymeric suspensions on a spouted bed of inert particles. Glass beads, ABS®, polypropylene (PP), and polystyrene (PS) were chosen as inert particles and were analyzed and characterized by their physicochemical properties. The polymeric suspensions were characterized by density, surface tension, rheology, and wettability. The fluid dynamic behavior of the bed was correlated with the particles and suspensions characteristics for each process: coating and drying. Each process performance was correlated with the polymeric suspension-particle work of adhesion.