A worldwide correlation for exponential bed particle size variation in subaerial aqueous flows

The particle size of the bed sediments in or on many natural streams, alluvial fans, laboratory flumes, irrigation canals and mine waste deltas varies exponentially with distance along the stream. A plot of the available worldwide exponential bed particle size diminution coefficient data against stream length is presented which shows that all the data lie within a single narrow band extending over virtually the whole range of stream lengths and bed sediment particle sizes found on Earth. This correlation applies to both natural and artificial flows with both sand and gravel beds, irrespective of either the solids concentration or whether normal or reverse sorting occurs. This strongly suggests that there are common mechanisms underlying the exponential diminution of bed particles in subaerial aqueous flows of all kinds. Thus existing models of sorting and abrasion applicable to some such flows may be applicable to others. A comparison of exponential laboratory abrasion and field diminution coefficients suggests that abrasion is unlikely to be significant in gravel and sand bed streams shorter than about 10 km to 100 km, and about 500 km, respectively. Copyright (C) 1999 John Wiley & Sons, Ltd.

A dynamic mathematical model for sequential leach bed anaerobic digestion of organic fraction of municipal solid waste

A mathematical model that describes the operation of a sequential leach bed process for anaerobic digestion of organic fraction of municipal solid waste (MSW) is developed and validated. This model assumes that ultimate mineralisation of the organic component of the waste occurs in three steps, namely solubilisation of particulate matter, fermentation to volatile organic acids (modelled as acetic acid) along with liberation of carbon dioxide and hydrogen, and methanogenesis from acetate and hydrogen. The model incorporates the ionic equilibrium equations arising due to dissolution of carbon dioxide, generation of alkalinity from breakdown of solids and dissociation of acetic acid. Rather than a charge balance, a mass balance on the hydronium and hydroxide ions is used to calculate pH. The flow of liquid through the bed is modelled as occurring through two zones-a permeable zone with high flushing rates and the other more stagnant. Some of the kinetic parameters for the biological processes were obtained from batch MSW digestion experiments. The parameters for flow model were obtained from residence time distribution studies conducted using tritium as a tracer. The model was validated using data from leach bed digestion experiments in which a leachate volume equal to 10% of the fresh waste bed volume was sequenced. The model was then tested, without altering any kinetic or flow parameters, by varying volume of leachate that is sequenced between the beds. Simulations for sequencing/recirculating 5 and 30% of the bed volume are presented and compared with experimental results. (C) 2002 Elsevier Science B.V. All rights reserved.

Characterizing the physical and chemical properties of a vermicompost filter bed

Vermicompost filtration is a new on-site waste treatment system. Consequently, little is known about the filter medium properties. The aim of this preliminary study was to quantify physical and compositional properties of vermicompost filter beds that had been used to treat domestic solid organic waste and wastewater. This paper presents the trials performed on pilot-scale reactors filled with vermicompost from a full-scale vermicompost filtration system. Household solid organic waste and raw wastewater at the rate of 130 L/m(2)/d was applied to the reactor bed surface over a four-month period. It was found that fresh casts laid on the bed surface had a BOD of 1290 mg/g VS while casts buried to a depth of 10 cm had a BOD of 605 mg/g VS. Below this depth there was little further biodegradation of earthworm casts despite cast ages of up to five years. Solid material in the reactor accounted for only 7-10% of the reactor volume. The total voidage comprised of large free-draining pores, which accounted for 15-20% of the reactor volume and 60-70% micropores, able to hold up water against gravity. It was shown that water could flow through the medium micropores and macropores following a wastewater application. The wastewater flow characteristics were modeled by a two-region model based on the Richards Equation, an equation used to describe porous spatially heterogeneous materials.

The use of cusum analysis in the early detection and management of hospital bed occupancy crises

Objective: To assess the value of cusum analysis in hospital bed management. Design: Comparative analysis of medical patient flows, bed occupancy, and emergency department admission rates and access block over 2 years. Setting: Internal Medicine Services and Emergency Department in a teaching hospital. Interventions: Improvements in bed use and changes in the level of available beds. Main outcome measures: Average length of stay; percentage occupancy of available beds; number of patients waiting more than 8 hours for admission (access block); number of medical patients occupying beds in non-medical wards; and number of elective surgical admissions. Results: Cusum analysis provided a simple means of revealing important trends in patient flows that were not obvious in conventional time-series data. This prompted improvements in bed use that resulted in a decrease of 9500 occupied bed-days over a year. Unfortunately and unexpectedly, after some initial improvement, the levels of access block, medical ward congestion and elective surgical admissions all then deteriorated significantly. This was probably caused by excessive bed closures in response to the initial improvement in bed use. Conclusion: Cusum analysis is a useful technique for the early detection of significant changes in patient flows and bed use, and in determining the appropriate number of beds required for a given rate of patient flow.

Local liquid holdups and hysteresis in a 2-D packed bed using X-ray radiography

An X-ray visualization technique has been used for the quantitative determination of local liquid holdups distribution and liquid holdup hysteresis in a nonwetting two-dimensional (2-D) packed bed. A medical diagnostic X-ray unit has been used to image the local holdups in a 2-D cold model having a random packing of expanded polystyrene beads. An aqueous barium chloride solution was used as a fluid to achieve good contrast on X-ray images. To quantify the local liquid holdup, a simple calibration technique has been developed that can be used for most of the radiological methods such as gamma ray and neutron radiography. The global value of total liquid holdup, obtained by X-ray method, has been compared with two conventional methods: drainage and tracer response. The X-ray technique, after validation, has been used to visualize and quantify, the liquid hysteresis phenomena in a packed bed. The liquid flows in preferred paths or channels that carry droplets/rivulets of increasing size and number as the liquid flow rate is increased. When the flow is reduced, these paths are retained and the higher liquid holdup that persists in these regions leads to the holdup hysteresis effect. Holdup in some regions of the packed bed may be an order of magnitude higher than average at a particular flow rate. (c) 2005 American Institute of Chemical Engineers

Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate. (c) 2005 Elsevier Ltd. All rights reserved.

Mechanics of raceway hysteresis in a packed bed

When a gas is introduced at high velocity through a nozzle into a packed bed, it creates a raceway in the packed bed. It has been found that the raceway size is larger when it is formed by decreasing the gas velocity from its highest value than when it is formed by increasing the gas velocity. This phenomenon is known as raceway hysteresis. A hypothesis has been oroposed to explain the hysteresis phenomenon based on a force-balance approach which includes frictional, bed-weight, and pressure forces. According to this hypothesis, the frictional force acts in different directions when the raceway is expanding and contracting. In this article, the entire packed bed has been divided into radial and Cartesian co-ordinate systems, and the forces acting on the raceway have been solved analytically for a simplified one-dimensional case. Based on the force-balance approach, a general equation has been obtained to predict the diameter of the raceway for increasing And decreasing velocities. A reasonable agreement has been found between the theoretical predictions and experimental observations. The model has also been compared with published experimental and plant data. The hysteresis mechanism in the packed beds can be described reasonably by taking into consideration the direction of frictional forces for the increasing- and decreasin-velocity cases. The effects of the particleshape factor and void fraction on the raceway hysteresis are examined.

Sheet flow sediment transport under waves with acceleration skewness and boundary layer streaming

The effect of acceleration skewness on sheet flow sediment transport rates (q) over bar (s) is analysed using new data which have acceleration skewness and superimposed currents but no boundary layer streaming. Sediment mobilizing forces due to drag and to acceleration (similar to pressure gradients) are weighted by cosine and sine, respectively, of the angle phi(.)(tau)phi(tau) = 0 thus corresponds to drag dominated sediment transport, (q) over bar (s)similar to vertical bar u(infinity)vertical bar u(infinity), while phi(tau) = 90 degrees corresponds to total domination by the pressure gradients, (q) over bar similar to du(infinity)/dt. Using the optimal angle, phi = 51 degrees based on that data, good agreement is subsequently found with data that have strong influence from boundary layer streaming. Good agreement is also maintained with the large body of U-tube data simulating sine waves with superimposed currents and second-order Stokes waves, all of which have zero acceleration skewness. The recommended model can be applied to irregular waves with arbitrary shape as long as the assumption negligible time lag between forcing and sediment transport rate is valid. With respect to irregular waves, the model is much easier to apply than the competing wave-by-wave models. Issues for further model developments are identified through a comprehensive data review.

Exploratory modelling of grinding pressure within a compressed particle bed

With increasing industry interest in high pressure roll grinding (HPGR) technology, there is a strong incentive for improved understanding of the nature of grinding pressure that exists in the interior of a compressed particle bed. This corresponds to the crushing region of the HPGR. The relationship between applied pressure (stress) to the particle bed and induced pressure (stress) within particles and at contact points between particles is of particular interest. A detailed parametric investigation is beyond the scope of this exploratory paper. However, this exploratory investigation does suggest some interesting behaviour. The compressed particle bed within an 80 turn diameter piston has been modelled using Particle Flow Code for three dimensions. PFC3D is a discrete element code. The total number of simulated particles was 1225 and 2450 for two beds of different thickness. Particle diameters were uniformly distributed between 4 and 4.5 mm. The results of the simulations show that stress intensity within the simulated particle beds and within the observed particles increased with increase of the applied stress. The intensity of the average vertical stress in the selected particles tended to be comparable with the intensity of the pressure applied to the surface of particle bed and was only occasionally higher. However, the stress at contact points between particles could be several times higher. In a real crusher, such high stress amplification at contacts will quickly decrease due to local crushing and a resultant increase the size of the contact area. Therefore, its significance is likely to be relatively small in an industrial context. The modelling results also suggest that failure within the particle bed will progress from the crushing surface towards the depth of the bed. (c) 2006 Elsevier Ltd. All rights reserved.