Relating Liquid Location as a Function of Contact Time Within a Porous Coating Structure to Optical Reflectance

Refractive index differences between a first and a second fluid can be utilised to obtain information about the location and amount of the fluids in a porous medium in the case where the light absorption coefficient of the skeletal material is small and the light scattering coefficient high using optical measurement methods. An example of such a medium is an air-filled paper coating, and the fluid that of a printing ink liquid phase absorbing into the coating during printing. We examined capillary absorption of mineral oil, used in offset printing ink, into model coatings compressed from dispersed mineral pigments with a range of latex binder levels, and established a porosity-normalised relationship for light reflectance change as a function of absorbed mass of the liquid established at a given time after initial contact with the liquid. The results suggest a significant change in reflectance due to the absorption, and progressive absorption behaviour of the liquid in the coatings can be monitored by the change in reflectance following a newly established relationship derived from the observational data. The findings support the concept of a preferred pathway flow for the wetting front, defined by differential pore size and connectivity, and a longer time saturation front flow lagging behind the wetting front, which theoretically at the limit of infinite time coincides with the wetting front, the time constant of the approach being related to the permeability of the porous network.     

Investigation on mass diffusion process in porous media based on Lattice Boltzmann method

The mass diffusion process inside a porous medium is difficult for numerical simulation due to complex and stochastic nature of its structure. Based on the lattice Boltzmann method and reconstruction technology, this article presents an approach for simulating mass diffusion process and predicting the effective mass diffusivity in porous media, which is validated by comparing theoretical and experimental data. The concentration distribution and effective mass diffusivity inside porous media can be obtained.     

Spontaneous Inertial Imbibition in Porous Media Using a Fractal Representation of Pore Wall Rugosity

Considering the separable phenomena of imbibition in complex fine porous media as a function of timescale, it is noted that there are two discrete imbibition rate regimes when expressed in the Lucas–Washburn (L–W) equation. Commonly, to account for this deviation from the single equivalent hydraulic capillary, experimentalists propose an effective contact angle change. In this work, we consider rather the general term of the Wilhelmy wetting force regarding the wetting line length, and apply a proposed increase in the liquid–solid contact line and wetting force provided by the introduction of surface meso/nanoscale structure to the pore wall roughness. An experimental surface pore wall feature size regarding the rugosity area is determined by means of capillary condensation during nitrogen gas sorption in a ground calcium carbonate tablet compact. On this nano size scale, a fractal structure of pore wall is proposed to characterize for the internal rugosity of the porous medium. Comparative models based on the Lucas–Washburn and Bosanquet inertial absorption equations, respectively, for the short timescale imbibition are constructed by applying the extended wetting line length and wetting force to the equivalent hydraulic capillary observed at the long timescale imbibition. The results comparing the models adopting the fractal structure with experimental imbibition rate suggest that the L–W equation at the short timescale cannot match experiment, but that the inertial plug flow in the Bosanquet equation matches the experimental results very well. If the fractal structure can be supported in nature, then this stresses the role of the inertial term in the initial stage of imbibition. Relaxation to a smooth-walled capillary then takes place over the longer timescale as the surface rugosity wetting is overwhelmed by the pore condensation and film flow of the liquid ahead of the bulk wetting front, and thus to a smooth walled capillary undergoing permeation viscosity-controlled flow.     

Determination of Permeability Distributions Using NMR Velocity Imaging

This study develops a methodology for determining the absolute permeability distribution in a porous media sample using velocity data obtained from NMR imaging experiments. An objective function describing the discrepancy between observed and simulated data is reduced by iteratively updating the permeability. This parameter estimation scheme is based on an iterative method which uses optimal control theory to refine the estimates. Although this theory is developed for both isotropic and anisotropic porous media, the permeability reconstructions examined in this paper are restricted to the isotropic case. Synthetic data are used to investigate the impact of varying the noise in the experimental data, the degree of parameterization, the relative weighting of the regularization term in the objective function, and the amount and type of data required to obtain a satisfactory permeability reconstruction. These synthetic data are extracted from the solution of numerical experiments that have utilized an assumed permeability distribution. The methodology is also applied to data gathered in laboratory experiments for water flow in a sandstone sample.     

Interrelationship between Resistivity Index,Capillary Pressure and Relative Permeability

It is known that the three important parameters, resistivity, capillary pressure, and relative permeability, are all a function of fluid saturation in a porous medium. This implies that there may be a correlation among the three parameters. There have been many papers on the approach to inferring relative permeability from capillary pressure data. However, the literature on the interrelationship between resistivity index, capillary pressure, and relative permeability has been few. The models representing such relationships have been proposed in this study, including a new model correlating relative permeability and capillary pressure. Some of the models were verified using experimental data for the first time. It has been shown that the other two parameters could be determined using these models if one of the three parameters (capillary pressure, relative permeability, and resistivity) is known. Using this approach, it would be possible to quickly obtain a distribution of capillary pressure and relative permeability characteristics as a function of depth and location across an entire reservoir.     

Efficiency of Capillary Imbibition Dominated Displacement of Nonwetting Phase by Wetting Phase in Fractured Porous Media

The critical and optimum injection rates as well as the critical fracture capillary number for an efficient displacement process are determined based on the experimental and numerical modeling of the displacement of nonwetting phase (oil) by wetting phase (water) in fractured porous media. The efficiency of the process is defined in terms of the nonwetting phase displaced from the system per amount of wetting phase injected and per time. Also, the effects of injection rate on capillary imbibition transfer dominated two-phase flow in fractured porous media are clarified by visualizing the experiments. The results reveal that as the injection rate is increased, fracture pattern begins to become an effective parameter on the matrix saturation distribution. As the rate is lowered, however, the system begins to behave like a homogeneous system showing a frontal displacement regardless the fracture configuration.     

多孔材料填充薄壁结构吸能的相互作用效应

研究多孔材料填充薄壁结构的相互作用效应产生的机理,并建立了表征模型. 以泡沫 铝填充帽形结构为例,发现压溃的填充物分为致密区、过致密区和未变形区3个区域. 基于 理想可压缩假设建立了填充多孔材料分析模型,获得各区域体积变化和等效应变等关系;结 合薄壁结构超叠缩单元模型,对填充结构各组分的能量吸收进行了拆分. 研究表明,薄壁结 构的吸能略有增加,多孔材料的吸能增加40{\%}左右. 过致密区的形成是相互作用效应的 主要原因.     

Non-linear Model for Wood Saturation

The paper presents a non-linear model of saturation with fluid of anisotropic capillary porous bodies and the results of experimental investigations of wood saturation with methacrylate. The obtained experimental curves illustrating the distribution of methacrylate in wood samples allow the estimation of material coefficients and verification of the theoretical model. The theoretical model is developed based on the balance equations of mass, momentum, and energy, and the thermodynamics of irreversible processes. The non-linear differential equation, describing the distribution of methacrylate content in wood and its evolution during the saturation is solved numerically. The theoretical curves obtained on the basis of both linear and non-linear models are compared with the experimental data and better agreement between them for the non-linear model is stated.     

On Determining the Percolation Reynolds Number and the Characteristic Linear Dimension for Ideal and Fictitious Porous Media

Various versions of representations of the percolation Reynolds number for porous media with isotropic and anisotropic flow properties are considered. The formulas are derived and the variants are analyzed with reference to model porous media with a periodic microstructure formed by systems of capillaries and packings consisting of spheres of constant diameter (ideal and fictitious porous media, respectively). A generalization of the Kozeny formula is given for determining the capillary diameter in an ideal porous medium equivalent to a fictitious medium with respect to permeability and porosity and it is shown that the capillary diameter is nonuniquely determined. Relations for recalculating values of the Reynolds number determined by means of formulas proposed earlier are given and it is shown that taking the microstructure of porous media into account, as proposed in [1, 2], makes it possible to explain the large scatter of the numerical values of the Reynolds number in processing the experimental data.     

Petrophysical and Capillary Properties of Compacted Salt

This paper reports experimental results that demonstrate petrophysical and capillary characteristics of compacted salt. The measured data include porosity, gas permeability, pore size distribution, specific surface area, and gas-brine breakthrough and capillary pressure. Salt samples employed in the experiments were prepared by compacting sodium chloride granulates at high stresses for several hours. They represent an intermediate consolidation stage of crushed salt under in-situ conditions. The porosity and permeability of compacted salt showed similar trends to those expected in backfilled regions of waste repositories excavated in salt rock. The correlation between the measured porosity and permeability seems to be independent of the compaction parameters for the range examined in this study. The correlation also shows a different behaviour from that of rock salt. The data of all petrophysical properties show that the pore structure of compacted salt can be better characterized by fracture permeability models rather than capillary bundle ones. Simple creep tests, conducted on the fully-brine-saturated compacted salt samples, yielded similar strain rates to those obtained by a steady-state mechanical model developed from the tests on fully brine-saturated granular salt. A modified procedure is proposed for the evaluation of restored-state capillary pressure data influenced by the material creep. The characteristic parameters for the capillary behaviour of compacted salt are determined by matching the Brooks-Corey and van Genuchten models with the measured data. The Leverett functions determined with different methods agree well.     

Nondestructive damage detection in structures using changes in compliance

A methodology to identify damage in a structure is presented in this paper. The method utilizes a new form of damage index based on the changes in the distribution of the compliance of the structure due to damage. The changes in the compliance distribution are obtained using the mode shapes of the pre-damaged and the post-damaged state of the structure. The validity of the method is demonstrated using numerically generated data from beam structures and experimental data from a free–free beam structure with inflicted damage. In the numerical and experimental examples, the damage identification performance of the proposed method is compared with that of the existing strain-energy-based method. The results of the numerical and experimental studies indicate that the proposed compliance-based damage index method can be used in damage identification of the structure.     

Limit Models of Pore Space Structure of Porous Materials for Determination of Limit Pore Size Distributions Based on Mercury Intrusion Data

This paper proposes the application of capillary and chain random models of pore space structure for determination of limit pore diameter distributions of porous materials, based on the mercury intrusion curves. Both distributions determine the range in which the pore diameter distribution of the investigated material occurs and defines the degree of inaccuracy of the method based on the mercury intrusion data caused by the indeterminacy of the sample shape and its pore space architecture. We derived equations describing the quasi-static process of mercury intrusion into the porous layer and porous ball with a random chain pore space structure and analysed the influence of the model parameters on the mercury intrusion curves. It was shown that the distribution of link length in the chain model of the pore space, random location of chain capillaries in the sample and the length distribution of the capillaries do not influence significantly the intrusion process. Therefore, a simple model of the mercury intrusion into the layer is proposed in which chain links of the pore space have random diameters and constant length. This model is used as a basic model of the intrusion process into a sample of any shape and size and with homogeneous and isotropic chain pore space architecture. The thickness of the layer then represents the mean length of chain capillaries in the sample. It was also proved that the capillary and chain models of pore space architecture are limit models of the network model identified in this paper with the pore architecture of the investigated sample. This justifies the application of both models for determination of limit cumulative distributions of pore diameters in porous materials based on the mercury intrusion data.

     

Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network

A stochastic approach to network modelling has been used to simulate quasi-static immiscible displacement in porous media. Both number-based and volume-based network saturation results were obtained. Number-based results include: number-based saturation curves for primary drainage, secondary imbibition and secondary drainage, fluid distribution data, and cluster trapping history. Using pore structure data of porous media, it is possible to convert the number-based curves to capillary pressure — saturation relationships. Pore size distribution functions and pore shapes which are thought to closely represent Berea sandstone samples were used to predict the capillary curves. The physical basis of these calculations is a one-to-one correspondence between the cumulative node and bond index fractions in the network analysis, and the cumulative number-based distributions of pore body and pore throat diameters, respectively. The oil-water capillary pressure curve simulated for primary drainage closely resembles those measured experimentally. The agreement between the simulated and the measured secondary imbition and secondary drainage curves is less satisfactory.     

Capillary Pressures by Fluid Saturation Profile Measurements During Centrifuge Rotation

A novel centrifuge technique to obtain the capillary pressure curve by measuring the local fluid distribution in a spinning core is presented. The Nuclear Tracer Imaging Centrifuge (NTIC) method measures the fluid saturation profile along the length of the core to directly obtain the capillary pressure curve. The proposed method is superior to conventional centrifuge techniques because (1) the capillary pressure curve is obtained at one rotational speed, (2) core plugs are not removed from the spinning centrifuge for imaging, and (3) no mathematical solution is needed to calculate the capillary pressure curve. The literature states that the various mathematical solutions used in conventional centrifuge tests are the greatest source of error, not the uncertainty in the experimental data. By eliminating the dependence of such solutions, the NTIC represents an alternative to conventional centrifuge tests, and may be used to validate the various mathematical procedures applied in conventional centrifuge capillary pressure tests. NTIC may also confirm the applicability of other imaging techniques that rely on core plug removal for saturation imaging, by verifying if there is no fluid re-distribution at static conditions.     

A New Method for Calculating Two-Phase Relative Permeability from Resistivity Data in Porous Media

Many resistivity data from laboratory measurements and well logging are available. Papers on the relationship between resistivity and relative permeability have been few. To this end, a new method was developed to infer two-phase relative permeability from the resistivity data in a consolidated porous medium. It was found that the wetting phase relative permeability is inversely proportional to the resistivity index of a porous medium. The proposed model was verified using the experimental data in different rocks (Berea, Boise sandstone, and limestone) at different temperatures up to 300°F. The results demonstrated that the oil and water relative permeabilities calculated from the experimental resistivity data by using the model proposed in this article were close to those calculated from the capillary pressure data in the rock samples with different porosities and permeabilities. The results demonstrated that the proposed approach to calculating two-phase relative permeability from resistivity data works satisfactorily in the cases studied.     

A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media

In the past decades, there was considerable controversy over the Lucas–Washburn (LW) equation widely applied in capillary imbibition kinetics. Many experimental results showed that the time exponent of the LW equation is less than 0.5. Based on the tortuous capillary model and fractal geometry, the effect of tortuosity on the capillary imbibition in wetting porous media is discussed in this article. The average height growth of wetting liquid in porous media driven by capillary force following the [`(L)] _s(t) ~ t^1/2D_T{\overline L _{\rm {s}}(t)\sim t^{1/{2D_{\rm {T}}}}} law is obtained (here D _T is the fractal dimension for tortuosity, which represents the heterogeneity of flow in porous media). The LW law turns out to be the special case when the straight capillary tube (D _T = 1) is assumed. The predictions by the present model for the time exponent for capillary imbibition in porous media are compared with available experimental data, and the present model can reproduce approximately the global trend of variation of the time exponent with porosity changing.     

A model of acoustic absorption in fluids based on a continuous distribution of relaxation times

This work extends the quasi-equilibrium relaxation theory of sound absorption in liquids to the case of continuous distribution of relaxation times. Such extension is needed when absorption mechanisms are not confined to the action of viscosity and heat conduction, but are mainly due to the excitation of a large number of internal molecular degrees of freedom. In this case the conventional Navier-Stokes equations are not sufficient to describe the fluid motion, and additional equations are required to model normal relaxation stresses. When relaxation frequencies form a sufficiently dense distribution, as is the case for many biological fluids, it makes sense to consider the limit of continuously distributed relaxation frequencies, in order to obtain the required equation for normal relaxation stresses.In contrast to its discrete counterparts, the proposed method avoids the use of a potentially infinite number of relaxation equations for a given set of distinct relaxation frequencies. Instead, these are replaced by a single evolution equation of Boltzmann type whose right-hand side is a linear combination of the time derivatives of density and entropy. The rheological functions appearing before these derivatives are expressed in terms of the absorption coefficient. Since the dependence of absorption coefficient on sound frequency is measurable experimentally, these rheological coefficients can be recovered from experimental data.The key feature of the present study is that a closed system of equations of motion can be formulated directly from absorption measurement data on the basis of the theory proposed for the very wide range of absorption laws that can occur in practice.As an illustration of the generality of the present method, a number of absorption laws documented in the experimental literature are considered in detail, in order to derive the coefficients of the related systems of equations of motion for these liquids. For example, the methodology based on modelling of acoustic absorption in biologically soft tissue by the employment of fractional derivatives, which has been recently developed in the literature, is shown to be a special case of the proposed theory.     

Theoretical and experimental aspects of vacuum impregnation of porous media using transparent etched networks

Vacuum impregnation is a process method in which air and native solution are removed from the porous space of a given porous material and replaced by an external solution. Vacuum impregnation is divided into two steps: Firstly, the porous material is immersed in a liquid solution and exposed to subatmospheric pressure for a given time to ensure that air trapped in the porous materials will be removed; secondly, atmospheric pressure is re-established and the external solution penetrates the pore structure of the porous material. The objective of this study was to describe the hydrodynamic mechanisms involved in vacuum impregnation of porous materials as a function of capillary number and viscosity ratio. To achieve the objectives proposed in the present study, a transparent glass micromodel 7.7 cm × 7.4 cm was first constructed using the photolithographic technique. In addition, a stainless steel vacuum tank was built. The tank top was covered with a transparent reinforced glass plate. The whole system was connected to a vacuum pump, and a conventional video camera was adapted to record the experiments. Liquid saturation was determined through the image analysis process. Capillary number and viscosity ratio were determined for the drainage and imbibition processes. For the systems studied, we conclude that transport mechanisms ranged between stable displacement and capillary fingering during the vacuum step (drainage) while transport mechanisms ranged between continuous capillary and discontinuous capillary domains during the atmospheric step (imbibition). Earlier work indicated that our proposed process should be even more efficient for realistically large systems.