Cathy J. Ridgway

Practical observation of deviation from Lucas-Washburn scaling in porous media

Abstract This work analyses the applicability of the Lucas–Washburn equation to experimental observations of imbibition into real network structures. The experimental pore structures used in this study are constructed from tablets of two finely ground calcium carbonates, with defined differences in particle size distribution. These are compressed under a range of different applied pressures to achieve a controlled series of porosities while maintaining the surface chemical, particulate and morphological pore characteristics constant. The porosities are determined by mercury intrusion porosimetry applying corrections for mercury compression and penetrometer expansion together with a correction for sample skeletal compression (Gane et al., J. Am. Chem. Soc., 35 (1996)). Imbibition studies are made by bringing each porous sample into contact with a supersource of liquid and the dynamic imbibition is recorded gravimetrically. Results follow a long timescale macroscopic absorption rate depending on the square root of time but show a failure to scale according to pore size in the Lucas–Washburn equation even though the constants of surface energy, contact angle and fluid viscosity have been maintained. Furthermore, values of average measured pore radius are shown to be finer than the Lucas–Washburn predicted equivalent hydraulic capillary radius. The predominance of a relevant pore size within a given pore size distribution forming a selective pathway filling based on inertial retardation of larger pores and short-term linear time wetting in finer pores is argued to account for the departure from simple pore size scaling.

Dynamic absorption into simulated porous structures

Abstract A computer model, pore-cor 1 , has been used to simulate the permeation of fluid into porous structures by applying a wetting algorithm for fluids undergoing both inertial and viscous dynamical absorption. These structures comprise cubic pores connected by cylindrical throats on a three-dimensional 10×10×10 position matrix. Previously, pore-cor has been used to simulate the void structure of porous media by fitting as closely as possible the simulated mercury intrusion curve of the model structure to that of the experimentally determined mercury intrusion curve of the actual sample. This refined model structure was then used to simulate the absorption of a number of different fluids and confirmation with experimental absorption data, adopting the same fluid, provided the necessary confidence in the model. Based on this practical experience, the framework is developed from experimental comparison so that pore-cor can now be applied as a ‘predictor’ tool rather than a simulator of existing experimental results. The structures used here have been generated with the aim of isolating certain parameters so their influence on the absorption behaviour of a fluid can be identified. It is shown how, keeping the porosity constant, structures can be represented in a number of different ways and that these structures will have vastly different absorption behaviour. Reducing the value of the fluid density in the simulation has also been investigated to show where the transition occurs in the absorption behaviour from the linear t-dependent short timescale inertial Bosanquet regime to the √t Lucas–Washburn (LW) viscous regime. Such a system of connecting pores is representative of pigmented paper coating structures and, for example, by changing the particle size distribution of the pigment under suitably modified calendering conditions, pore structures of equal porosity could exist in practice and have drastically different effects on fluid absorption. Implications on, say, the way an ink would set on the coating surface, can have dramatic practical significance. To be able to predict these effects and to design optimal coating structures for the fluids and inks used in a variety of printing, lacquering and glueing processes is seen as a significant advance, obviating the need for expensive matrix-designed production trialling.

The effects of correlated networks on mercury intrusion simulations and permeabilities of sandstone and other porous media

Abstract A void space network is presented for the simulation of mercury intrusion and the calculation of the absolute permeability of porous media. Mercury intrusion is simulated by the Laplace/Washburn equation within a percolation algorithm. A ‘Dinic’ operational research network analysis algorithm gives the maximal flow capacity of the unit cell. A combination of the Darcy and Poiseuille equations of flow is then used to derive the absolute gas permeability of the simulated structure. Mercury intrusion curves and permeabilities are calculated for networks with banding, clustering of small pores and throats, or clustering of large pores and throats. The modelling method is then applied to banded sandstone samples with edge corrections, and it is shown that the constraint of fitting to experimental mercury intrusion data suppresses the permeability differences induced by structural changes alone. The same networks can model mercury hysteresis, porosity, connectivity, pore/throat size correlation, tortuosity and other properties, and can be applied to any consolidated porous medium.

Effect of particle size distribution and packing compression on fluid permeability as predicted by lattice-Boltzmann simulations

Abstract Massive parallel lattice-Boltzmann method simulations of flow through highly polydispersed spherical particle packings formed using Monte-Carlo methods were performed. The computed fluid permeabilities were compared to experimental data obtained from blocks made of three natural ground calcium carbonate powders compressed at different levels. The agreement with experimental measurements is excellent considering the approximations made. A series of flow simulations was also performed for packings of spherical particles compressed at different levels with increasing polydispersity modeled with both lognormal and Weibull size distributions. The predicted permeabilities were found to follow reasonably well the Carman–Kozeny correlation although an increasing deviation towards lower predicted permeabilities with increasing polydispersity was observed. Finally, following a careful analysis of the inherent numerical errors, an expression relating the Kozeny “constant” to the size distribution and compression level was derived from the simulation results, which led to a modified correlation.

Absorption Rate and Volume Dependency on the Complexity of Porous Network Structures

Results of simulated supersource imbibition into model network structures are compared with experimental observations of real network structures determined by dynamical gravimetric fluid uptake. A computer model, Pore-Cor, has been used previously to simulate the imbibition of fluid into porous structures by applying an imbibition algorithm for fluids undergoing both inertial and viscous dynamical absorption (Schoelkopf et al., 2000). The structures comprise cubic pores connected by cylindrical throats on a three-dimensional 10 × 10 × 10 position matrix. The absorption curves for model structures with monosized pore and throat size ranges and for polydisperse pore and throat size distributions centred around 0.1 µm, increasing from 0.1 µm as a lower limit, and decreasing from 0.1 µm as an upper limit, respectively, are analysed. A relevant observable porosity and 50% volume intrusion radius (r50) are obtained using simulated mercury intrusion. Experimental network pore structures were made using compressed tablets, formed under a series of pressures, of two finely ground calcium carbonates with defined differences in skeletal particle size distribution. The surface chemical, particulate and morphological pore characteristics were maintained constant over a range of porosities using controlled wet grinding and careful use of dispersant levels such that the ratio of dispersant to BET surface area was held constant. The experimental porosities were determined by mercury intrusion porosimetry applying corrections for mercury compression and penetrometer expansion together with a correction for sample skeletal compression (Gane et al., 1996). The applicability of the Lucas–Washburn equation is examined by defining two equivalent hydraulic radii, one based on a Darcy absorption length (rehcDarcy) and the other on a volume uptake (rehc), respectively. The results from the model structures having distributions of pores and throats, which contain either small or large pores, respectively, follow the experimental results qualitatively. Both approaches show a long timescale macroscopic absorption rate depending approximately, but not exactly, on the square root of time. The two experimental series, however, fail to scale with each other via the Lucas–Washburn equation in accordance with pore size, r50. Porosity is shown to be the main factor determining the volume absorption rate, and, when used as a weighting factor, gives linear correlation-scaling between r50 and a derived volume-based r′ehc equivalent hydraulic radius, obtained from an analytical expression of the observed Darcy-based rehcDarcy. The experimental samples showed that the directly observed rehc and the calculated r′ehc, derived from Darcy length, were equal, but this was not the case for the model values. A factor β = r′ehc/r50 is shown to be a possible descriptor of the sample network complexity and an indicator for the probability level of pore filling during the absorption dynamic.

Modelling of the Void Space of Tablets Compacted Over a Range of Pressures

A previously developed computer model, named Pore‐Cor, has been used to simulate the changes in the void‐space dimensions which occur during the compaction of tablets over a range of pressures.

Modelling of simulated clay precipitation within reservoir sandstones

The purpose of this study was to investigate whether a previously developed computer model, named Pore-Cor, could simulate the subtle changes in void space dimensions which occur during the artificial deposition of small amounts of illite and kaolinite within Fontainebleau sandstone. Clay precipitation was carried out by placing a sandstone plug in a gold capsule, with an aluminosilicate gel, and treating the plug hydrothermally with potassium hydroxide solution. Using experimental conditions of 350°C and 1.0 kbar (100 MPa), illite, illite-smectite and kaolinite were precipitated in parts of the sandstone void space with morphologies similar to those of authigenic clay minerals in sandstone petroleum reservoirs. Mercury intrusion curves were then measured for the untreated and clay precipitated sandstones. The Pore-Cor package simulated these intrusion curves, and generated void space models of the correct porosity. By this means, subtle changes in void space dimensions and connectivity could be identified, which give rise to large changes in permeability.

Influence on Pore Structure of Micro/Nanofibrillar Cellulose in Pigmented Coating Formulations

Nano and microfibrillated cellulose (NFC and MFC, respectively, collectively termed MNFC) is known to interact strongly with water, related to its high polarity and surface area. The swelling behaviour acts to form a gel with high water retention properties. The observation that nanocellulose could possibly be used in paper or other coating formulations, as a co-binder, for example, raises a question about the possible effects it could have on coating pore structure. In this study, we analyse the pore structure of pigmented coatings, liquid absorption and permeability, in respect to the influence of partially substituting traditional co-binder carboxymethyl cellulose with MNFC. The contrast between polar water and non-polar liquid, such as alkane, is used to probe the water interactive and extractable in-coating (internal) gel-formation properties of the nanocellulosic materials. These contrasting liquids are important in many processes, such as offset printing, but also in respect to exposure of coatings in general to environmental factors in application. Results show that permeability to liquid water is dramatically reduced when nanocellulosic material is present, though water can permeate by diffusion through the nanocellulose gel network. Long timescale exposure to water during absorption leads to extraction of any soluble salts remaining after the chemical treatment of the fibrillar material during production. Inert alkane, on the other hand, can absorb and permeate freely without interactive hindrance from the nanocellulose, with no extractive effect. Such a construct could in principle be considered for use as an oil-water differential membrane or for slow release concepts in aqueous systems by loading soluble deliverable materials within the nanocellulosic gel.

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.

Short timescale inkjet ink component diffusion: An active part of the absorption mechanism into inkjet coatings

The structures of inkjet coatings commonly contain a high concentration of fine diameter pores together with a large pore volume capacity. To clarify the interactive role of the porous structure and the coincidentally occurring swelling of binder during inkjet ink vehicle imbibition, coating structures were studied in respect to their absorption behaviour for polar and non-polar liquid. The absorption measurement was performed using compressed pigment tablets, based on a range of pigment types and surface charge polarity, containing either polyvinyl alcohol (PVOH) or styrene acrylic latex (SA) as the binder, by recording the liquid uptake with a microbalance. The results indicate that, at the beginning of liquid uptake, at times less than 2 s, the small pores play the dominant role with respect to the inkjet ink vehicle imbibition. Simultaneously, water molecules diffuse into and within the hydrophilic PVOH binder causing binder swelling, which diminishes the number of active small pores and reduces the diameter of remaining pores, thus slowing the capillary flow as a function of time. The SA latex does not absorb the vehicle, and therefore the dominating phenomenon is then capillary absorption. However, the diffusion coefficient of the water vapour across separately prepared PVOH and SA latex films seems to be quite similar. In the PVOH, the polar liquid diffuses into the polymer network, whereas in the SA latex the hydrophobic nature prevents the diffusion into the polymer matrix and there exists surface diffusion. At longer timescale, permeation flow into the porous coating dominates as the resistive term controlling the capillary driven liquid imbibition rate.