Washburn Equation Research Articles

CFD analysis of pore morphology, gravity, and fluid characteristics influences on water flooding process

In this research, computational fluid dynamics (CFD) was employed to examine the two-phase flow of water and oil in a porous medium. For this purpose, the Navier-Stockes equations, which describe fluid motion, and the Cahn-Hillard phase field, which defines the interface between two phases, are coupled. The numerical discretization system of equations was solved using the finite element method (FEM) with the COMSOL software. To validate the results and the phase-field model (PFM), the Lucas and Washburn equation was used together with the experimental data. Through this study, the effective parameters were evaluated in two parts. In the first part, seven models with different pore morphologies were designed, and the impact of petrophysical parameters of the reservoir, including the shape of pores, connectivity of pores with or without throat lines, porous media heterogeneity, and relative permeability, on oil recovery was investigated. The second part was devoted to performing sensitivity analysis on the effect of fluid properties, including interfacial tension, wettability, viscosity ratio, injected fluid flow, and gravity, upon enhanced oil recovery (EOR) in different morphologies. Owing to the uniform distribution of capillary pressure in the patterns with the throat lines, the sweep efficiency of the injected fluid was found to be better, and thereby oil production increased. The results of the present work proved the significant influence of gravity on EOR, so that by applying gravity to the solution domain, the breakthrough time and oil recovery factor increased by 20 minutes and 28.6 %, respectively. Moreover, the velocity of the injected fluid as a representative of the flow rate had the greatest effect on EOR, with a 35 % increase in production.

Wetting and pressure gradient performance in a lattice Boltzmann color gradient model

An accurate implementation of wetting and pressure drop is crucial to correctly reproduce fluid displacement processes in porous media. Although several strategies have been proposed in the literature, a systematic comparison of them is needed to determine the most suitable for practical applications. Here, we carried out numerical simulations to investigate the performance of two widely used wettability schemes in the lattice Boltzmann color gradient model, namely, the geometrical wetting scheme by Leclaire et al. [Phys. Rev. E 95(3), 033306 (2017)](scheme-I) and the modified direction of the color gradient scheme by Akai et al. [Adv. Water Resour. 116, 56–66 (2018)] (scheme-II). We showed that scheme-II was more accurate in simulating static contact angles of a fluid droplet on a solid surface. However, scheme-I was more accurate in simulating a dynamic case of a binary fluid flow in a horizontal capillary tube described by the Washburn equation. Moreover, we investigated the performance of two popular pressure gradient implementation types. Type-I used the so-called Zou–He pressure boundary conditions at the inlet and the outlet of the domain, while type-II used an external body force as a pressure gradient. We showed that the type-I implementation was slightly more accurate in simulating a neutrally wetting fluid in a horizontal capillary tube described by the Washburn equation. We also investigated the differences between the two types of pressure gradient implementation in simulating two fluid displacement processes in a Bentheimer sandstone rock sample: the primary drainage and the imbibition displacement processes.

Research on the influence of dynamic contact angle of mercury meniscus on the interpretation of rock pore throat radius in mercury intrusion experiments

Addressing the lack of measurement methods for dynamic contact angles of mercury meniscus in mercury intrusion porosimetry experiments and the unclear understanding of the impact of dynamic contact angles on the interpretation of pore throat radius in rocks, a new type of closed mercury intrusion characteristic curve (O-R curve) is constructed utilizing the withdrawal curve O and the secondary injection curve R obtained from the experiments. Based on the excellent wetting and de-wetting correlation characteristics at the equal mercury saturation points on this curve, a method for measuring the dynamic contact angles of mercury meniscus (O-R loop method) is established. Taking the Chang 63 tight oil reservoir samples from the Nanliang Oilfield in the Ordos Basin of China as an example, this method is applied to investigate the dynamic contact angles of mercury meniscus in mercury intrusion porosimetry experiments and the impact on the interpretation of pore throat radius in rocks. The results indicate that the dynamic contact angles of mercury meniscus changes significantly during the experiments, which cannot be ignored. And the smaller pore throats lead to more severe deformation of mercury meniscus, resulting in higher wetting resistance coefficients and hysteresis angles. Calculations reveal that the pore throat radius interpreted using the modified Washburn equation (which adopts dynamic contact angles) are generally larger than those interpreted using the conventional Washburn equation (which adopts static contact angles), with relative errors ranging from 12.2% to 54.7%. The smaller the pore throats, the larger the relative errors. The analysis shows that the conventional Washburn equation significantly underestimates the reservoir pore throat radius due to the neglect of the dynamic contact angle, while the modified Washburn equation provides more accurate interpretation. Overall, this research provides a method for calculating the dynamic contact angle in mercury intrusion porosimetry experiments and has important reference significance for the accurate interpretation of rock pore throat radius.

Effect of physicochemical properties on critical sinking and attachment of respirable coal mine dust impacting on a water surface

Respirable coal mine dust (RCMD) inhalation is identified as the main cause of the resurgence of coal worker’s pneumoconiosis (CWP) since the mid-1990s. At present, the predominant dust control technology is the water spray system. However, in practice, the capture efficiency of RCMD by this technology is relatively low. To understand the capturing mechanism and develop improvement strategies, this research is focused on the surface chemistry study of RCMD and its impact on a water surface using a dynamic model. Proximate analysis, chemical, and mineral composition of a run-of-mine (ROM) coal sample from Appalachian region were analyzed using a proximate analyzer, Inductively Coupled Plasma Mass Spectrometry (ICP-MS), and X-ray Diffraction (XRD), respectively. Contact angles were measured by capillary rise test using the Washburn equation. Based on the dynamic model, the effects of particle size, density, contact angle, and surface tension on the critical sinking were investigated. It was pointed out in this work that reducing surface tension, in turn, decreases contact angle, which has been neglected in the literature. Regime maps for different minerals were created and showed that organic matter has the highest critical velocity due to its low density and high contact angle. Reducing water surface tension to the critical solid surface tension of coal around 30 mN/m could maximize the attachment efficiency. Scaling laws, constructed by force balance, led to the criteria of critical sinking: Ucr∼61-cosθ2D+1γlvρlR, i.e., Wecr∼121-cosθ2D+1. A semi-empirical formula for critical velocity was obtained by fitting the simulation data, Ucr=1.0961-cosθ2D+1γlvρlR. Attachment efficiency was defined and formulated as Pa=U02Ucr2=We0Wecr, establishing relationships between attachment efficiency and the physicochemical properties of RCMD and water droplets.

Study of the contact angle and roughness effects on mercury intrusion porosimetry (MIP) analysis in natural/real carbonate rocks using massive pure minerals and synthetic carbonate rocks

Studying pore networks in rocks is critical for understanding reservoir properties, with mercury intrusion porosimetry (MIP) being a key laboratory method. MIP involves capillary intrusion of mercury, with intrusion pressure (P) related to capillary diameter (d) by the Washburn equation, incorporating mercury properties like contact angle (θ) and surface tension (γ). While a constant contact angle of 140° is typically assumed for MIP, it can vary based on rock mineralogy and surface roughness. This study aims to analyze how contact angle variations and surface roughness affect MIP analysis of carbonate rocks. Initially, contact angle data was obtained for calcite, dolomite, and quartz with varying roughness levels. Synthetic rocks were then constructed using these minerals. MIP was performed using the typical 140° contact angle and a calculated contact angle from the Cassie model, which considers surface composition fraction. Natural rock MIP analysis followed, with contact angles varying due to mineral composition and roughness. The study found higher contact angles than the standard 140°, affecting pore size distributions up to 30%. Natural rock pore network curves were adjusted based on synthetic rock data analysis. These findings emphasize the need for accurate contact angle selection in MIP for precise pore distribution analysis and contribute to the further study of carbonate rocks.

Saturation Equation: An Analytical Expression for Partial Saturation during Wicking Flow in Paper Microfluidic Channels.

The design and fabrication of paper-based microfluidic devices is critically dependent on modeling fluid flow through porous paper membranes. A commonly observed phenomenon is partial saturation, i.e., regions of the paper membrane not being filled completely due to pores of different sizes. The most comprehensive model to date of partial saturation during wicking flow in paper is the Richards equation. However, the solution to the Richards equation requires numerical solvers like COMSOL, which makes it largely inaccessible to the paper microfluidics and lateral flow assay community. There is therefore a need for a simple and appropriate model of partial saturation in paper membranes, easily usable by the wider research community. In the current work, we present an approach to model paper membranes as a bundle of parallel capillaries whose radii follow a two-parameter log-normal distribution. Application of the Washburn equation to the bundle provides a distribution of fluid fronts, which can be used to calculate saturation. Using this approach, we developed the "saturation equation"─an explicit analytical expression to calculate saturation as a function of space and time in 1D wicking flow. Experimentally obtained data for spatiotemporal saturation for four different paper materials were fit to this analytical model to obtain parameters for each material. Results obtained from this analytical model match well with both experimental data and numerical results obtained from the Richards equation. The availability of an explicit analytical expression for partial saturation will enable incorporation of the critical phenomenon of partial saturation in the design of paper microfluidic devices.

Capillary filling of star polymer melts in nanopores

The topology of a polymer profoundly influences its behavior. However, its effect on imbibition dynamics remains poorly understood. In the present work, capillary filling (during imbibition and following full imbibition) of star polymer melts was investigated by molecular dynamics simulations with a coarse-grained model. The reversal of imbibition dynamics observed for linear-chain systems was also present for star polymers. Star polymers with short arms penetrate slower than the prediction of the Lucas–Washburn equation, while systems with long arms penetrate faster. The radius of gyration increases during confined flow, indicating the orientation and disentanglement of arms. In addition, the higher the functionality of the star polymer, the more entanglement points are retained. Besides, a stiff region near the core segments of the stars is observed, which increases in size with functionality. The proportion of different configurations of the arms (e.g., loops, trains, tails) changes dramatically with the arm length and degree of confinement but is only influenced by the functionality when the arms are short. Following full imbibition, the different decay rates of the self-correlation function of the core-to-end vector illustrate that arms take a longer time to reach the equilibrium state as the functionality, arm length, and degree of confinement increase, in agreement with recent experimental findings. Furthermore, the star topology induces a stronger effect of adsorption and friction, which becomes more pronounced with increasing functionality.

Investigation on spontaneous liquid–liquid imbibition in capillaries with varying axial geometries using lattice Boltzmann method

Spontaneous liquid–liquid imbibition in capillaries with irregular axial geometries is common in the petroleum industry. Monitoring the real-time dynamic contact angle (DCA) of the meniscus is crucial during such processes. In this work, we extend the Bell–Cameron–Lucas–Washburn (BCLW) equation by considering the axial shape of the capillaries, inertial force, and non-wetting fluid viscosity. We also develop a cascaded multi-component Shan–Chen lattice Boltzmann method (CLBM) with a modified mass-conservative curved boundary scheme to accurately simulate imbibition processes in sinusoidal capillaries. The results indicate that the DCA is highly sensitive to variations in the axial geometry of the capillary during imbibition, displaying a periodic time evolution pattern. When the axial geometry diverges, the DCA increases, and when it converges, the DCA decreases. The viscosity ratio affects the imbibition velocity, controlling the evolution period and extreme values of the DCA. A critical contact angle exists for a fixed capillary axial geometry and viscosity ratio. Continuous spontaneous imbibition occurs if the static contact angle is smaller than this critical value. However, if it exceeds this threshold, imbibition ceases within regions where axial geometry divergence. Moreover, we noticed a discrepancy in imbibition lengths predicted by the extended BCLW equation that ignores the DCA compared to those computed through the CLBM. To address this issue, we employed CLBM to monitor the DCA in real time and used the gathered data to refine the extended BCLW equation. As a result, the prediction of imbibition lengths by the extended BCLW equation for coupling the DCA became more accurate.

Reverse Washburn dynamics induces flow acceleration during capillary filling

We present a corollary to Washburn's equation in capillary dynamics. We show that, during capillary filling, in cases where flow path decreases with time, an accelerating capillary flow or reverse-Washburn flow regime occurs. We provide a description of this phenomenon following Washburn's classic analysis and characterize a “reverse-Washburn” capillary flow regime in both inertial and viscous regimes. This regime is observed and characterized in experiments and numerical simulations of recently discovered self-coalescence flows, opening the door to engineering devices with naturally accelerating capillary inflows.

Wetting and pressureless infiltration behavior of Cu/316L system at 1100°C

It is still one of the great challenges to fully understand the coupling of reactive infiltration kinetics and wetting mechanism in the pressureless infiltration processes. We studied the wetting and pressureless infiltration behavior of Cu on 316L substrate with different pore sizes and porosity at 1100 °C under high vacuum by using the sessile drop method. The initial contact angle of Cu/316L system is ∼ 26 °, and rapid spreading (in ∼1.35 s) occurs under the action of capillary force due to the dissolutive wetting mechanism. The passivated film (Cr2O3) on the surface of 316L stainless-steel removed by self-cleaning reaction and interface reaction accompanying CrO gas phase release. Further, the obstacles of wetting and infiltration were eliminated. The reactive infiltration kinetics of Cu/316L cannot be predicted by the Washburn equation, preferring to an exponential variation. The infiltration kinetics is consistent with the wetting kinetics of melt on the smooth substrate surface, that is, the infiltration kinetics is limited by the dissolution kinetics.

Water absorption characteristics in autoclaved aerated concrete, diatomite, and calcium silicate board

AbstractWater absorption into cementitious materials has been discussed to be anomalous because of the nonlinearity of cumulative water absorbed with the square root of time. In this study, the water absorption characteristics in porous materials such as autoclaved aerated concrete (AAC), diatomite, and calcium silicate board were examined focusing on the different pore structures and the gravity effect. The one‐dimensional water absorption into diatomite and calcium silicate board both from top and bottom surface can be explained by water flow under its own capillary pressure based on the Washburn equation. On the other hand, the cumulative water volume absorbed into AAC was not proportional to the square root of time. The effect of gravity affected the absorption rate but was small for the ultimate cumulative water volume absorbed in AAC. The moisture content near the top drying surface was only half of that near the bottom wetting surface. It was hypothesized that the capillary pores in AAC can be dried while the fine pores at nano meter scale can be saturated under the pore humidity near the drying surface. It is concluded that the anomaly of water absorption in AAC may be affected by complicated pore structures with fine pores as well as drying conditions opposite to wetting surfaces.

Influence of the Resin System and Sand Type on the Infiltration of 3D-Printed Sand Tools.

Binder jetting is a highly productive additive manufacturing (AM) method for porous parts. Due to its cost-effectiveness, it is used for large components and quantities ranging from prototyping to series production. Post-processing steps like sintering or infiltration are common in several applications to achieve high density and strength. This work investigates how 3D-printed sand molds can be infiltrated with epoxy resins without vacuum assistance to produce high-strength molds for thermoforming applications. Specimens 3D-printed from different sand types are infiltrated with resins of different viscosity and analyzed for infiltration velocity and depth. The infiltration velocities corresponded well with the correlation described in Washburn's equation: The resins' viscosities and the saturation level were decisive. Amongst the investigated sand types commonly used in foundries, sand type GS19 was found most suitable for infiltration. However, the sand type proved to be a less relevant influencing factor than the resins' viscosities and quantities applied. Infiltration of topology-optimized 3D-printed sand tools up to a wall thickness of 20 mm for thermoforming applications was found to be feasible.

Analyses of the effects of fiber diameter, fiber fibrillation, and fines content on the pore structure and capillary flow using laboratory sheets of regenerated fibers

Abstract The aim of this work is to investigate the influence of fiber fibrillation and fines on the pore structure of well-defined regenerated fiber sheets as well as the water flow through the sheet. For this purpose, sheets were produced with refined, fibrillated fibers only, with unfibrillated fibers and fines, as well as with fibrillated fibers and fines. Next, the samples were analyzed by brightfield and fluorescence microscopy, mercury porosimetry, and an ascending test. Both the fibrils and the added fines reach into the pores between the fibers or are deposited there. As a result, pore size decreases and capillary flow slows down. The two effects overlap when the fiber surface is fibrillated and fines are present. Sheets with thicker fibers form a pore structure with larger pores in between the fibers. However, such a change in pore size has no significant influence on the flow of water through the sheet in the performed ascending tests. It is shown that a statistical model with the parameters fibrillation and fines content can be used to describe the ascending rate nearly as well as the Lucas–Washburn equation. Consequently, the equation could be improved by the addition of further fiber and sheet properties.

New insights into pore fractal dimension from mercury injection capillary pressure in tight sandstone

Mercury injection capillary pressure (MICP) has been widely used for pore fractal dimension determination and thus leads to a variety of calculation models with different results. Here, taking the tight sandstone gas reservoir of Shaximiao Formation in Jinhua-Zhongtaishan area, central Sichuan Basin as the object, the theory, method and application of pore fractal dimension determination from MICP are explored. Based on Yu-Xia model and Washburn equation, rigorous analytical expressions on fractal dimension, capillary pressure and mercury saturation are deduced. After pre-processing including validation, consistency correction and shape-preserving interpolation, the fractal turning point is located with the local maximum of the front-back moving variance ratio of mercury saturation, and then the global, macropore and micropore fractal dimensions are determined respectively by nonlinear fitting. As suggested by the data processing results of the 39 MICP samples, there is no significant direct correlation between pore fractal dimensions and petrophysical properties represented by permeability. However, the combination of fractal model related parameters, especially global fractal dimension and entry pressure, can identify effectively reservoir quality ranks. Meanwhile, for gas layers with relatively high permeability, larger global fractal dimensions may imply roughly more favorable pore structure and better reservoir quality, while the total quality of the relatively low-permeability gas layers is poor and nearly independent of the fractal dimensions. The representative MICP-based pore fractal models, He-Hua and Shen-Li, are critically reviewed. The theoretical simplification and calculative approximate of these two models lead to some degree of error in pore fractal dimension determination, despite their slight correlation in the fitting results with those of the present model. This study may improve the understanding of the pore fractal dimension determined from MICP and provide reference for pore structure evaluation, reservoir quality classification and capillary pressure modeling.

Modeling of Paper-Based Bi-Material Cantilever Actuator for Microfluidic Biosensors.

This research explores the dynamics of a fluidically loaded Bi-Material cantilever (B-MaC), a critical component of μPADs (microfluidic paper-based analytical devices) used in point-of-care diagnostics. Constructed from Scotch Tape and Whatman Grade 41 filter paper strips, the B-MaC's behavior under fluid imbibition is examined. A capillary fluid flow model is formulated for the B-MaC, adhering to the Lucas-Washburn (LW) equation, and supported by empirical data. This paper further investigates the stress-strain relationship to estimate the modulus of the B-MaC at various saturation levels and to predict the behavior of the fluidically loaded cantilever. The study shows that the Young's modulus of Whatman Grade 41 filter paper drastically decreases to approximately 20 MPa (about 7% of its dry-state value) upon full saturation. This significant decrease in flexural rigidity, in conjunction with the hygroexpansive strain and coefficient of hygroexpansion (empirically deduced to be 0.008), is essential in determining the B-MaC's deflection. The proposed moderate deflection formulation effectively predicts the B-MaC's behavior under fluidic loading, emphasizing the measurement of maximum (tip) deflection using interfacial boundary conditions for the B-MaC's wet and dry regions. This knowledge of tip deflection will prove instrumental in optimizing the design parameters of B-MaCs.

Two level deacidification mathematical model for the description of transport of solid alkaline particles and diffusion of ions in a treated acid paper

Industrial progress in papermaking in the early nineteenth century led to the technologies that resulted in more acidic papers, which was caused mainly by the exploitation of alum (KAl(SO4)2) and rosin as sizing agents. The papers prepared by such technologies have degraded more quickly. From the 1930s various deacidification and preservation processes with basic agents have been developed. The most widespread deacidification process is with the aerosol (spray system) consisting of microscale particles MgO and perfluoroheptane (PFH) as a carrier (the so-called Bookkeeper process). The shortcomings of this process are the low dissolution of solid MgO particles and the transport to the interior of acidic paper. We have developed a theoretical two-level model of the Bookkeeper process suitable for prediction of deacidification extent. The model involves both the dissolution/reaction of the solid particles and transport of solvated ions and solid particles inside the bulk of paper. The developed model coincides with the results of the performed deacidification experiment. The model is also in good agreement with the Lucas–Washburn equation, which is usually used for the description of the penetration of a deacidifying agent into the paper.

Penetration Coefficients of Commercial Nanolimes and a Liquid Mineral Precursor for Pore-Imitating Test Systems—Predictability of Infiltration Behavior

Nanolimes have been commercially available for over a decade as a remineralization agent for natural stone to combat deterioration. While they have been applied successfully and studied extensively, their penetration abilities in different materials have not yet been readily quantifiable in situ and in real time. Using two transparent pore-imitating test systems (acrylic glass (PMMA) and polydimethylsiloxane (PDMS)) and light microscopy, the penetration coefficients (PCs) of two nanolimes (CaLoSiL (CLS) and Nanorestore Plus (NRP)), as well as their solvents, were determined experimentally in square channels of about 100 µm diameter. Their PCs and those for a previously published glass-resin-based test system were also predicted based on measurable material parameters or literature values using the Lucas-Washburn equation. Additionally, a liquid mineral precursor (LMP) of calcium carbonate based on complex coacervation (CC) was investigated as an alternative to the solid particle dispersions of nanolime. In general, the dispersions behaved like their pure solvents. Overall, trends could be reasonably well predicted with both literature and experimentally determined properties using the Lucas-Washburn equation. In absolute terms, the prediction of observed infiltration behavior was satisfactory for alcohols and nanolimes but deviated substantially for water and the aqueous LMP. The commercially available PMMA chips and newly designed PDMS devices were mostly superior to the previously published glass-resin-based test system, except for the long-term monitoring of material deposition. Lastly, the transfer of results from these investigated systems to a different, nontransparent mineral, calcite, yielded similar PC values independently of the original data when used as the basis for the conversion (all PC types and all material/liquid combinations except aqueous solutions in PDMS devices). This knowledge can be used to improve the targeted design of tailor-made remineralization treatments for different application cases by guiding solvent choice, and to reduce destructive sampling by providing a micromodel for pretesting, if transferability to real stone samples proves demonstrable in the future.

Laser Melt Infiltration of UHMWPE into the Binary Coatings of Strontium Apatite and Colloidal Silica

Medical-grade ultrahigh molecular weight polyethylene (UHMWPE) is the material of choice for sliding surfaces in various articular joint implants owing to its excellent biocompatibility and superior physical properties, such as an exceptionally low coefficient of friction and excellent durability. However, the bioinert nature of UHMWPE limits its extended use in rapidly advancing medical fronts. In this study, bioactive surface modifications of UHMWPE were addressed using a newly developed laser-melt infiltration technique. UHMWPE was coated with binary mixtures of strontium apatite and colloidal silica particles and irradiated using a 30 W CO2 laser to reach the maximum temperature of 150 ± 5 °C. UHMWPE melts infiltrated the porous matrices of the coatings by capillary force and formed surface-selective composite materials between them. Capillary rise heights were evaluated by observing the uplift of the substrate after the selective dissolution of the coating substances and were found to be much higher than the estimated values based on the Lucas–Washburn equation. This finding suggests that the melt viscosity of UHMWPE confined within the nanopores might be significantly lower than that measured at macroscopic scales. Both strontium and silicate ions are known osteo-inductive factors, and their concentrations eluted from the binary coatings were substantially higher than those found in the single coatings.

Capillary Imbibition in Layered Sandstone

Spontaneous capillary imbibition in rocks is fundamental to numerous geomorphological processes and has caused numerous engineering problems. Sedimentary rocks are widely distributed across the Earth’s surface and usually bear layer structures that make the pore structure anisotropic. Understanding the effects of the anisotropic pore structure on capillary imbibition in sedimentary rocks is crucially important but remains inadequate, especially on larger scales than a single tube. In this study, the capillary imbibition process in sandstone was monitored by measuring the water absorption mass, height of the water absorption front, NMR (nuclear magnetic resonance) T2 spectra, and stratified moisture distribution. The results demonstrate that (1) the layer structure had a significant effect on the capillary imbibition process by altering water absorption rate and water redistribution mode, as the time of the water front reaching the top of Sample A1 lagged behind Sample A2 by 500 min; (2) vapor diffusion and condensation occurred ahead of the water-absorption front, which was more obvious in samples with well-developed beddings; (3) in sandstone samples with bedding planes perpendicular to the height (Per samples), internal water migration lagged behind superficial water migration and was longer in sandstones with well-developed beddings, such as the case of Sample A2, for which the time lag was as large as 280min. Based on a combination of observations of the sandstone structure at pore scale and layer scale with results calculated from the Lucas–Washburn equation, we propose the concept of the representative pore-structure element (RPE). Based on analysis on water migration in RPEs, we suggest that the effects of the layer structure on capillary imbibition in sandstone are embedded in the different water migration modes in Par (samples with bedding planes parallel to the height) and Per samples. The water migration mode in Par samples can be simplified as primary upward intra-layer migration followed by intra-layer horizontal migration, while that in Per samples is primary intra-layer horizontal migration followed by intra-layer upward migration.

Slag resistance mechanism of MgO–Mg2SiO4–SiC–C refractories containing porous multiphase aggregates

The slag resistance of MgO–SiC–C (MSC) refractories should be improved because of the mismatch in the thermal expansion coefficient between the aggregates and matrix, as well as the defects caused by the affinity between periclase and slag. In this study, MgO–Mg2SiO4–SiC–C (MMSC) refractories were prepared using porous multiphase MgO–Mg2SiO4 (M-M2S) aggregates to replace dense fused magnesia aggregates. Compared to MSC, the slag penetration index of MMSC decreased by 43.5%. The structure of the porous aggregates increased the surface roughness, and the multiphase composition of the aggregates decreased the mismatch of the thermal expansion coefficient with the matrix, thus reducing debonding between the aggregates and matrix. The aggregates and matrix in the MMSC formed an interlocking structure, which bound them more tightly to improve the slag resistance. The slag viscosity at different depths from the initial slag/refractory interface was calculated using the Ribond model. The M-M2S aggregates increased SixOyz− in the slag, which increased the slag polymerization and slag viscosity. The aggregates and matrix in the MMSC reacted with the slag to form high melting point phases, which reduced the channel of the slag. In addition, the penetration depth and velocity derived from the Washburn Equation were modified for the CaO–SiO2–Al2O3–MgO–FeO slag and magnesia based refractory to accurately evaluate slag penetration.