Review of Flow through Porous Media as Applied to Head Loss in Water Filters

This article reviews the development of our understanding of flow through porous media with a focus on understanding the clean-bed head loss in water filters. A model of the Forchheimer form is developed by typing existing empirical models to current hydrodynamic theory, and constants are developed for three filter media: glass beads, crushed silica sand, and crushed anthracite coal. Suggestions are made for future research that would improve our understanding.     

Volumetric Clarifying Filtration of Urban Source Area Rainfall Runoff

Volumetric clarification is a common storm-water unit operation for hydrologic attenuation that couples particulate matter (PM) separation. Recent volumetric clarification can also include integrated filtration. This study examines the unsteady hydraulic and head loss response of a volumetric clarifying filter (VCF) system to urban source area hydrologic loadings in Baton Rouge, La for 19 fully captured events. The rainfall-runoff response of the 1,088?m2 paved watershed is examined as a direct VCF loading. Watershed responses yielded two classes of behavior; high volume events with an equilibrium volumetric runoff coefficient from 0.6–0.8 while low volume events were 0.4–0.6. Runoff PM as suspended sediment concentration (SSC) yielded coarse heterodisperse influent particle-size distributions (PSDs); transformed to finer and more monodisperse PSDs after treatment. While event-mean head loss is less than 25 mm, instantaneous values up to 200 mm were dependent on instantaneous flow to the filters. Without backwashing, filter ripening head loss is small due to the coarse uniform filter media and radial filter configuration, with a loss of 2% porosity across the series of 19 events. Despite filter ripening an Ergun model was capable of predicting head loss across the entire flow rate range. Head loss and flow frequency distributions were exponential. Results indicate that a volumetric clarifier, filter geometry, and engineered media combination are capable of reducing effluent SSC to <30?mg/L through serial mechanisms of sedimentation followed by filtration.     

CFD Modeling of Particulate Matter Fate and Pressure Drop in a Storm-Water Radial Filter

This study examined a common form of filtration, a passive radial cartridge filter (RCF) system, to physically separate hetero-disperse particulate matter in rainfall-runoff. The RCF tested utilizes aluminum-oxide coated media with a uniform pumice substrate (d50m = 3.56?mm) gradation. To examine the RCF, this study applied laser diffraction and real-time pressure sensor measurements to validate a computational fluid dynamics (CFD) model to predict particle separation and filter head loss for hetero-disperse particulate matter (PM). Filter hydrodynamics are resolved using a macroscopic approach for the porous media with a k-ε turbulence model coupled with the Ergun equation. PM fate was resolved using a discrete phase model. CFD results closely followed measured data for filtration and head-loss response for all flow rates. With influent PM at 200?mg/L (d50m = 16.3?μm), effluent PM ranged from 32?to?57?mg/L for surface loading rates of 24?to?189?L/m2?min, respectively. There was agreement between measured and modeled data for effluent PM and head loss. CFD postprocessing provided added insight into the mechanistic behavior of the RCF by means of three-dimensional hydraulic profiles, particle trajectories, and pressure distributions, illustrating that a RCF is nonuniformly loaded. As part of design and regulation, such physical testing coupled with modeling is a required precursor to uncontrolled field testing, regular maintenance and certification of a BMP.     

废胶粉改性沥青微表处性能试验研究

分析了影响废胶粉改性沥青性能主要因素包括混合温度、混合时间、胶粉加入量及SBS添加剂,通过试验确定最佳油石比并进行废胶粉改性沥青混合料车辙试验、劈裂试验、浸水马歇尔试验。试验数据表明在各影响因素的最佳条件下进行废胶粉改性沥青性能试验,确定最佳油石比为4.73时废胶粉改性沥青混合料的车辙试验、劈裂试验、浸水马歇尔试验满足规范要求且优于基质沥青混合料路用性能。     

A mathematical model of aluminum depth filtration with ceramic foam filters: Part I. Validation for short-term filtration

This work presents a mathematical model to compute the efficiency of depth filtration of molten aluminum using ceramic foam filters. In the model, the porous structure of foam filters was represented by a unit cell that takes into account the convergent-divergent nature of the flow field. The steady, two-dimensional, and fully developed flow field within the unit cell was obtained from the numerical solution of the continuity and Navier-Stokes equations. The assessment of the proper assumptions for the model was carried out by comparing the computed velocity field with that experimentally determined for a physical model of the unit cell with scale 10:1 and containing an aqueous solution of CaCl₂. The measurements were done using the particle image velocimetry (PIV) technique. The efficiency and the coefficient of initial filtration for foam filters were obtained from the determination of the particle limiting trajectory, resulting from a force balance on a spherical inclusion. This balance included the buoyancy and the viscous drag forces. The last force took into consideration the wall effect on the particle motion. The values of the computed initial filtration coefficient show an excellent agreement with the corresponding measured ones reported for laboratory and plant tests for short-term filtration. This comparison involves several combinations of particle sizes and downward fluid superficial velocities. This model is further extended to study long-term filtration in the second part of the article.     

Urban Particle Capture in Bioretention Media. I: Laboratory and Field Studies

Bioretention is a novel stormwater best-management practice that uses a mixture of soil/sand/mulch as adsorptive filtration media that can capture both urban particulates and dissolved pollutants while promoting infiltration. This study conducted a series of laboratory column experiments and field observations, which showed that: (1) bioretention media stratification occurs with runoff percolation due to particulate deposition; (2) bioretention filter media are clogging limited, instead of breakthrough limited; and (3) both depth filtration and cake filtration significantly contribute to urban particle capture. Because of the fine size of bioretention media, incoming suspended solids cannot significantly penetrate below 5–10?cm of the media in the column tests and approximately 20?cm in the monitored field facility. Bioretention filters under intermittent flow conditions exhibited higher solids loading capacity (in kg/m2) before clogging than under continuous flow conditions. The clay components in incoming total suspended solids assume critical responsibility for bioretention media clogging. The media resistance due to solids deposition was estimated through Darcy’s law. The hydraulic conductivity of two media types decreased from 54±23 and 72±46?cm/h to less than 10?cm/h due to particle capture. Experimental results suggest that a 20-cm media depth is sufficient for bioretention design and maintenance procedures (media replacement) for runoff particle capture.     

Urban Particle Capture in Bioretention Media. II: Theory and Model Development

As a novel stormwater best-management practice, using a soil/sand/mulch mixture to capture urban pollutants while promoting infiltration, the unique media composition renders bioretention significantly different from conventional sand filters. In this work, a three-layer model is presented to describe particulate capture in bioretention media employing parameter calibration and presensitivity analysis. Since the fine size of bioretention media strictly limits the particulate penetration distance, the media column is modeled as a pristine zone (bottom), a working zone (middle), and a cake zone (top). Mechanisms of both depth filtration and cake filtration are examined through mass balances, which show that both are significant. The developed resistance of each layer due to solid deposition was also estimated. Experimental data for different media/TSS-type combinations of selected experimental trials were used in parameter calibration. The calibrated model successfully predicted the effluent TSS and media hydraulic conductivity of subsequent trials with appropriate boundary and initial conditions as input. A weighted combination of calibrated parameters from different TSS types also agreed well with media behavior for treating a complex TSS mixture. The results of media replacement (top removal and refill) simulation also reasonably fit experimental data. Using proper assumptions, a long-term scenario analysis for permeability reduction was performed for a field bioretention facility. Based on modeling results, this study recommends a shallow bioretention media depth design, an annual or biannual field inspection schedule, and periodic media replacement maintenance.     

Constriction-Based Retention Criterion for Granular Filter Design

The filter design criteria in practice are currently based on laboratory tests that were carried out on uniform base soil and filter materials. These criteria mostly involve specific particle size ratios, where the system of base soil and filter is represented by some characteristic particle sizes. Consequently, these criteria have limitations when applied to nonuniform materials. In filters, it is the constriction size rather than the particle size that affects filtration. In this paper, a mathematical procedure to determine the controlling constriction size is introduced, and subsequently, a constriction-based retention criterion for granular filters is presented. The model also incorporates the effect of nonuniformity of base soil in terms of its particle size distribution, considering the surface area of the particles. The proposed retention criterion is verified based on experimental data taken from past studies plus large-scale filtration tests carried out by the authors. The model successfully and distinctly demarcates the boundary between effective and ineffective filters in the case of cohensionless base soils.     

Evaluation of Alternative Media for Pebble Matrix Filtration Using Clay Balls and Recycled Crushed Glass

Protecting slow sand filters (SSFs) from high-turbidity waters by pretreatment using pebble matrix filtration (PMF) has previously been studied in the laboratory at University College London, followed by pilot field trials in Papua New Guinea and Serbia. The first full-scale PMF plant was completed at a water-treatment plant in Sri Lanka in 2008, and during its construction, problems were encountered in sourcing the required size of pebbles and sand as filter media. Because sourcing of uniform-sized pebbles may be problematic in many countries, the performance of alternative media has been investigated for the sustainability of the PMF system. Hand-formed clay balls made at a 100-year-old brick factory in the United Kingdom appear to have satisfied the role of pebbles, and a laboratory filter column was operated by using these clay balls together with recycled crushed glass as an alternative to sand media in the PMF. Results showed that in countries where uniform-sized pebbles are difficult to obtain, clay balls are an effective and feasible alternative to natural pebbles. Also, recycled crushed glass performed as well as or better than silica sand as an alternative fine media in the clarification process, although cleaning by drainage was more effective with sand media. In the tested filtration velocity range of (0.72–1.33)??m/h and inlet turbidity range of (78–589) NTU, both sand and glass produced above 95% removal efficiencies. The head loss development during clogging was about 30% higher in sand than in glass media.     

Weld Metal Microstructure Prediction in Submerged Arc Weld Metal of C‐Mn Steel

The prediction model has been developed for steel weld metal microstructural constituents as a function of flux ingredients such as CaO, MgO, CaF₂ and Al₂O₃ in submerged arc welding carried out at fixed welding parameters. The results of quantitative measurements of micro‐structural constituents on eighteen weld metal samples were utilised for developing the prediction equations of microstructural constituents applying statistical design of experiment for mixtures. Among the flux ingredients, CaO appears to be most important as an individual as well as interaction with other ingredients viz. CaF₂ and Al₂O₃ in influencing the amount of microstructural constituents in weld metal. The prediction equations have been checked for adequacy by performing tests on welding using randomly designed flux and found satisfactory. The iso‐response curves were developed for selected microstructural constituents to show their output levels at different percentage of flux ingredients.     

Air Binding of Granular Media Filters

Air bubbles that form in water treatment filters create headloss and can form whenever the total dissolved gas pressure exceeds the local solution pressure. The location of potential bubble formation in filters can be predicted based on measurements of the clean bed headloss with depth, flow rate, and the influent total dissolved gas concentration. Bubble formation within filters can be reduced by increasing the pressure within the filter via greater submergence (water head above the media), lower hydraulic flow rate, or using a more porous media. Bubbles trapped in the bed can be released by “burping,” which can reduce the extent of headloss buildup. Burping is more significant at lower flow rates and within a lower density, higher porosity, hydrophobic anthracite layer.     

Dynamic Modeling of Bentazon Removal by Pseudo-Moving-Bed Granular Activated Carbon Filtration Applied to Full-Scale Water Treatment

A model for the removal of pesticides by granular activated carbon (GAC) filtration in full-scale water treatment is presented. The model describes GAC filtration in a pseudo-moving-bed configuration, where two filters are operated in series and after breakthrough the first filter is regenerated and becomes the second filter. The influent of the second filter is changing due to gradual breakthrough of the first filter. Therefore, a dynamic model is developed based on kinetics, equilibrium, and mass balance equations. The model is calibrated and validated on data of full-scale and pilot plants. Operational strategies are evaluated of two different cases. From this study it can be concluded that a dynamic mathematical model can be successfully used to evaluate the performance and operation of full-scale GAC filters for pesticide removal and can be used for operational decision support. Data obtained from practice can be used for calibration without additional laboratory work.     

Enhanced Ripening of Slow Sand Filters

While successful in removing turbidity and pathogens from drinking water, slow sand filters require ripening periods at the beginning of each filter run. The premise of this research was that it should be possible to enhance the ripening of slow sand filters. Potential ripening agents were screened by assessing their interaction with the surface of filtration media and turbidity particles. Four natural organic polymers and nine synthetic polymers were investigated for their potential to enhance filter ripening. Of the 13 modifying agents considered, none conclusively sorbed to the filter media, and only one, a synthetic polymer, interacted with kaolin particles. A filter modified with continuous feed of the polymer ripened successfully and produced water with turbidity below 1.0 NTU in about 24 h. Most turbidity removal in the treated filter occurred in the schmutzdecke rather than within the depth of the filter bed. Hence, the mechanism of enhanced ripening in this case probably was particle agglomeration with resulting acceleration of particle deposition at the filter surface accompanied by straining or attachment to previously removed particles.     

Direct simulation of initial filtration phenomena within highly porous media

Initial filtration phenomena within highly porous filter media—ceramic foam filters (CFF) —were simulated by numerically solving the Navier-Stokes equations and the general transport equation for suspended particles. In this approach, a “piece” of the highly porous filter was modeled directly by constructing a calculation domain such that the main average geometrical properties of the real filters were embodied therein. The governing equations were then solved by imposing appropriate boundary conditions on the solid surfaces of the filter webs. The influences of Reynolds, Peclet, and Gravitational numbers, as well as filter porosity, on initial filtration efficiencies were investigated in this simulation. Predicted results were spotchecked against data from industrial filtration trials conducted by the authors for aluminum melts and found to be in good agreement.     

Effect of Media Grain Shape on Particle Straining during Filtration

This paper investigates how straining mechanisms of angular media (crushed limestone) provide improved filtration performance compared to rounded media (river stone). Columns of granular media were set in resin, sectioned, photographed, and digitized to produce a three-dimensional model of pore space geometry. This process was repeated for four filter media, each representing different grain shapes or packing densities. From measured pore throat distributions, a stepwise particle movement model was used to estimate the maximum volume of particles that could be stored in the bulk of the filter media. The results showed that the more angular the media, the wider the range of particle sizes that could be strained in the bulk of the filter. The stepwise model was applied only to individual particles; trapping of colloidal particles was not considered. However, when individual particles are too small to be strained, the same pore throat trapping contributes to the physical capture of avalanches and flocculates. Thus the findings of this work are relevant to deep bed filtration applications where headloss results from straining, such as storm-water best management practices or soil filters.     

Design of Minimum Seepage-Loss Nonpolygonal Canal Sections with Drainage Layer at Shallow Depth

Analytical solutions exist for the seepage discharge from polygonal and nonpolygonal canal sections underlain by a drainage layer at a hydraulically infinite depth. These solutions lead to underestimation of the seepage discharge if a drainage layer occurs at a shallow depth. This paper presents solutions for seepage discharge from circular and exponential sections overlying a shallow drainage layer. The discharge has been calculated by a finite-difference-based numerical solution of the differential governing the seepage flow. The phreatic boundaries of the flow domain were described in terms of two parameters that were estimated by a minimization process. Such seepage computations were performed for a large number of independent dimensionless variables of the section geometry. Subjecting the computed seepage to regression analyses, explicit equations for seepage discharge loss have been obtained. Using these seepage loss equations, the design variables for minimum seepage loss have been obtained. The use of the design equations has been illustrated by design examples.     

Electromagnetically Modified Filtration of Aluminum Melts—Part I: Electromagnetic Theory and 30 PPI Ceramic Foam Filter Experimental Results

In the present work, laboratory-scale continuous filtration tests of liquid A356 aluminum alloy have been performed. The tests were conducted using standard 30 PPI (pores per inch) ceramic foam filters combined with magnetic flux densities (~0.1 and 0.2 T), produced using two different induction coils operated at 50 Hz AC. A reference filtration test was also carried out under gravity conditions, i.e., without an applied magnetic field. The obtained results clearly prove that the magnetic field has a significant affect on the distribution of SiC particles. The influence of the electromagnetic Lorentz forces and induced bulk metal flow on the obtained filtration efficiencies and on the wetting behavior of the filter media by liquid aluminum is discussed. The magnitudes of the Lorentz forces produced by the induction coils are quantified based on analytical and COMSOL 4.2^® finite element modeling.     

Effects of Adsorbed Water Layer in Predicting Saturated Hydraulic Conductivity for Clays with Kozeny–Carman Equation

Saturated hydraulic conductivity for clays predicted using the conventional Kozeny–Carman equation is scalar and found to diverge significantly from measured values. The divergence is consistent and systematic requiring a mathematical derivation of the formula using first principles. The incorporation of the physical characteristics of the adsorbed water layer surrounding a clay particle results in a generalized Kozeny–Carman equation with two new parameters. The porosity correction factor gives the effective porosity taking into account the thickness of the adsorbed water layer and the mass specific surface area of the clay. The second parameter is shown to depend on the interparticle contact area and the interparticle contact stress. The ability of the proposed physically based generalized Kozeny–Carman equation to explain the results from some of the published laboratory permeability tests is tested. The paper results in a new theoretical framework to model changes in saturated hydraulic conductivity in clays where the soil profile is compacting as a result of changes in pore-water pressure and or externally applied loads.     

Flexural Capacity of Compact Composite I-Girders in Positive Bending

Current American Association of State Highway and Transportation Officials (AASHTO) bridge specifications for compact composite steel girders in positive bending with adjacent compact pier sections limit the allowable maximum strength to a value between the full plastic moment and the hypothetical yield moment of the cross section as a function of the depth of web in compression. The strength prediction equations derived using these methods provide conservative values when compared to the results of the parametric studies used to develop the equations. Recent experimental tests coupled with finite-element analysis and mechanistic evaluations of the cross-section flexural capacity suggest that larger capacities may be achieved than those determined from AASHTO’s prediction equations. This paper presents an assessment of the behavior of composite positive bending specimens. A summary of a comprehensive literature review is provided coupled with results of the analytical and experimental evaluation of the nominal moment capacity of composite girders. Lastly, a less conservative design moment capacity expression developed from this assessment is provided.     

Design of Minimum Seepage Loss Canal Sections with Drainage Layer at Shallow Depth

This paper presents an analytical solution for the quantity of seepage from a rectangular canal underlain by a drainage layer at shallow depth. The solution has been obtained using inverse hodograph and conformal mapping. Using the solution for the rectangular canal and the existing analytical solutions for triangular and trapezoidal canals, simplified algebraic equations for computation of seepage loss from these canals, when the drainage layer lies at finite depth, have been presented, which replace the cumbersome evaluation of complex integrals. Using these seepage loss equations and a general uniform flow equation, simplified equations for the design variables of minimum seepage loss sections have been obtained for each of the three canal shapes by applying a nonlinear optimization technique. The optimal design equations along with the tabulated section shape coefficients provide a convenient method for design of the minimum seepage loss section. A step-by-step design procedure for rectangular and trapezoidal canal sections has been presented.