A population balance model for high shear granulation

In a previous paper, Hoornaert et al. ( Powder Technol. 96 (1998); 116-128) presented data from granulation experiments performed in a 50 L Lödige high shear mixer. In this study that same data was simulated with a population balance model. Based on an analysis of the experimental data, the granulation process was divided into three separate stages: nucleation, induction, and coalescence growth. These three stages were then simulated separately, with promising results. It is possible to derive a kernel that fit both the induction and the coalescence growth stage. Modeling the nucleation stage proved to be more challenging due to the complex mechanism of nucleus formation. From this work some recommendations are made for the improvement of this type of model.     

Evaluation of increased denitrification in an anoxic activated sludge using zeolite

Zeolite added activated sludge unit (ZU) under anoxic conditions improved nitrate removal efficiency by 48% (i.e., equivalent to approximately 10 mg//) greater than that of a conventional activated sludge unit (CU) regardless of varying C/N ratio ranging from 0 to 4.8. For a C/N ratio of 4, no significant differences of denitrification rate were found between two units showing a range of 6.7 to 6.9 mg NO ₃ ^- -N/g VSS (volatile suspended solids) hr. However, a C/N ratio decrease to 1.6 was ascribed to considerable differences in denitrification rate showing 4.15 mg NO ₃ ^- -N/g VSS ·hr for the ZU, which was 39% greater than that of the CU presenting at 2.98 mg NO ₃ ^- -N/g VSS ·hr. It was decided that the presence of greater concentration of MLVSS (mixed liquor suspended solids) in the ZU can be efficiently used for enhanced denitrification as a potential carbon source due to autolysis, although a lower concentration of COD (i.e., less than 1.6 of C/N ratio) is introduced.     

基于相群平衡模型的浮选气泡聚并模拟

气泡尺寸分布直接影响气浮分离效率,而聚并是导致气浮池内气泡尺寸变化的主要因素。首先用实验方法测量气浮接触区气泡尺寸分布,然后用计算流体力学方法对气泡/水两相流动及气泡聚并进行模拟,最后通过对实验和数值模拟结果进行对比建立基于相群平衡模型的浮选气泡聚并行为的模拟方法,分别运用Luo、Free molecular和Turbulent聚并模型对气浮接触区气泡聚并行为进行模拟。结果表明:Turbulent聚并模型计算所得气泡尺寸分布与实验值最接近,适合模拟接触区气泡聚并;气泡平均直径随高度升高先变大后保持不变,气泡聚并主要发生在接触区中下部;气泡的加入增强了接触区流动混乱程度,上部产生对称涡流,中下部呈由边壁向中心的水平流动。     

Estimation of air concentration in dissolved air flotation (DAF) systems using a simple predictive tool

Dissolved air flotation (DAF) has been used for several decades in water treatment systems. It is a unit operation for the separation of solid and semisolid (floc) particles from a liquid phase that has been used for the clarification of potable water. The removal is achieved by dissolving air in the water or wastewater under pressure and then releasing the air at atmospheric pressure in a flotation tank or basin. The increased dissolved air concentration in water at elevated pressure is the fundamental principle that allows the formation of microbubbles. In this article a simple predictive tool is developed to estimate air saturated concentration in dissolved air flotation (DAF) systems. Estimations are found to be in excellent agreement with reported data in the literature with average absolute deviation being around 0.5%. The tool developed in this study can be of immense practical value for process engineers to have a quick check of air concentration in dissolved air flotation systems (DAF) at various conditions without opting for any experimental trials. In particular, water practitioners and process engineers would find the proposed approach to be user-friendly with transparent calculations involving no complex expressions.     

Population balance modelling of activated sludge flocculation: Investigating the size dependence of aggregation, breakage and collision efficiency

This paper describes the application of population balance models to activated sludge flocculation. It presents the development and selection of appropriate expressions for aggregation and breakage mechanisms within the population balance framework to describe the evolution of mean size and mass distribution of flocs under shear-induced conditions. To describe the flocculation process, 16 models with different size dependent aggregation and breakage expressions were compared and the kinetic parameters of aggregation rate constant and selection rate constant were extracted by fitting each model to the experimental data. Of the 16 models, the shear-induced aggregation and size-dependent selection model was found to best describe the experimental data, however there were some discrepancies between the model and experimental results at long experimental times. A size dependent collision efficiency was introduced into the aggregation expression and this improved the fitting of the model with the experimental data. However, the relationship between the kinetic parameters and shear rate did not follow expected physical relationships. Further improvements to the model were made by setting the aggregation rate constant proportional to shear rate and the selection rate size independent whilst still including the size-dependent collision efficiency. The aggregation rate constant, selection rate constant and critical size were extracted by fitting the model to the experimental data. This model was able to follow the change in mean size and evolution of mass and was used to predict other experimental data successfully. The modelling results indicated that the population balance model is a useful tool to describe the dynamics of activated sludge flocculation.     

腐殖活性污泥对SBR工艺降解污染物的影响研究

介绍了腐殖活性污泥处理技术在国内外的发展情况,对在SBR工艺及投加腐殖土填料形成腐殖活性污泥的SBR工艺降解污染物效果进行了对比分析,结果表明：投加腐殖土填料对SBR工艺去除COD的效果没有明显影响,但可缩短COD的降解时间;投加腐殖土填料的SBR反应器对N和P去除效果明显优于普通SBR工艺。     

Characteristics of adsorption and biodegradation of dissolved organic carbon in biological activated carbon pilot plant

The dissolved organic carbon (DOC) properties for the influent of the BAC pilot plant have shown a 42% biodegradable fraction and a 58% non-biodegradable fraction. The biodegradable dissolved organic carbon (BDOC) was degraded entirely by biodegradation; the removal efficiency was 65–83%. The BDOC removal efficiency at empty bed contact time (EBCT) 15 minutes was larger than at EBCT 8 minutes. At increasing EBCT, a more slowly biodegradable fraction of BDOC (H₂) was utilized. The non-biodegradable dissolved organic carbon (NBDOC) was removed mostly by adsorption, and the removal amount was 24–58%. Therefore, the DOC was removed by adsorption and biodegradation; the removal efficiency by biodegradation was 31%, and that by adsorption was 24%. The breakthrough behaviors of DOC and NBDOC continued to be saturated as the bed volume increased, whereas the BDOC breakthrough curves maintained a certain ratio according to the bed volume.     

Simulation of heterotrophic storage and growth processes in activated sludge under aerobic conditions

In this work, an extension of the Activated Sludge Model No. 3 (ASM3) is presented which takes oxygen transfer, microbial maintenance, and biomass decay into account, in order to describe the heterotrophic storage and growth processes in activated sludge. The sensitivity of the effluent chemical oxygen demand and oxygen uptake rate to the stoichiometric and kinetic coefficients was analyzed. Model calibration was successfully performed by comparing measured and predicted values for model components. Thereafter, the model was evaluated with the experimental results of four independent case studies. Results show that the established model is able to better and mechanistically describe the heterotrophic storage and growth processes in activated sludge.     

Simulation of population balance model-based particulate processes via parallel and distributed computing

Population Balance Models (PBMs), a class of integro partial differential equations, are utilized for simulating dynamics of numerous particulate systems. PBMs describe the time evolutions and distributions of many particulate processes and their efficient and quick simulation are critical for enhanced process control and optimization, especially for real-time applications. However, their intensive computational resource requirement is largely a prohibitive factor in the utility of PBMs for control and optimization. This paper describes how distributed computing systems may be leveraged to execute PBM-based simulations thus achieving time savings, using MATLAB's Distributed Computing Toolbox. A parallel computing algorithm was developed for a three dimensional and four dimensional population balance model with built-in constructs such as SPMD that ran efficiently on a cluster of two quad-core machines linked via a gigabit ethernet cable. Speedup of 6.2 and 5.7 times were achieved with 8 workers, over an un-parallelized code, for a 3 and 4 dimensional PBM respectively. Evaluations on work efficiency and scalability further affirm the algorithms’ respectable performance on larger clusters despite significant memory transfer overheads.     

A comparative adsorption/biosorption of phenol to granular activated carbon and immobilized activated sludge in a continuous packed bed reactor

The potential use of Mowital B30H resin immobilized dried activated sludge as a substitute for granular activated carbon for removing phenol from aqueous solution was examined in a continuous packed bed reactor as a function of flow rate and inlet phenol concentration. The working sorption pH value was determined as 1.0 for both the sorbents, and packed bed sorption studies were performed at this pH value. The maximum specific uptakes, total adsorbed quantities, and total removals of phenol related to the effluent volumes were determined by evaluating the breakthrough curves obtained at different flow rates and different inlet phenol concentrations for each sorbent. At the lowest flow rate of 0.8 mL/min and at the inlet phenol concentration of 500 mg/L, the maximum specific uptakes and total removals of phenol were 84.0 mg/g and 27.6%, respectively, for granular activated carbon and 9.0 mg/g and 9.3%, respectively, for immobilized dried activated sludge. Data confirmed that total removals of phenol decreased with increasing flow rate and inlet phenol concentration for both immobilized dried activated sludge and granular activated carbon systems.     

Effect of clinoptilolite addition and solids retention time on the extracellular polymeric substances composition and soluble chemical oxygen demands in activated sludge

This study was carried out to compare EPS (Extracellular Polymeric Substances) composition between conventional activated sludge (AS) and activated sludge dosed with clinoptilolite (CAS). Additionally, those were compared with organic removal efficiency in the effluent in conjunction with EPS concentrations. The experiments were conducted at SRT (Solids Retention Time) ranging from 5 to 100 d. For the CAS, proteins were more readily observed for SRT 20 and 100 d compared to that of the AS. Polysaccharide concentration in the sludge was greatly increased for the CAS, but it was significantly diminished when the SRT was extended. The level of EPS concentration observed from the effluent had the same pattern of variation for the two different types of systems. Regardless of type of reactor, the ratio of proteins for sludge versus effluent was independent of SRT, but the ratio of polysaccharides diminished as SRT increased. In the long run, the degree of protein synthesis directly ascribed to concurrent enhancement of SCOD removal efficiency was slightly more in the CAS. It was decided that clinoptilolite added system could be more reliably retrofitted to a conventional activated sludge process.     

Model-evaluation of the erosion behavior of activated sludge under shear conditions using a chemical-equilibrium-based model

The primary particles would erode from the sludge surface under shear conditions. As the primary particles have significant effects on the solid–liquid separation process, the erosion behaviors of activated sludge in biological wastewater treatment processes under shear conditions were investigated using a chemical-equilibrium-based model. The equilibrium dispersed mass concentration of the primary particles in the sludge solution was found to nonlinearly increase with the solid content and shear intensity, and could be well described by the model. Compared with other sludge reported in literatures, the activated sludge used in this study was found to be more stable during the shear test, with a high equilibrium constant K⁰ of 30.2 and a low Gibbs’ free energy of adhesion (ΔG⁰) of −3.41 at a shear intensity of 800 s⁻¹. The two parameters could be used to evaluate the strength of the sludge. The negative value of ΔH indicates the energy demand for the erosion process. The low value of ΔH for the activated sludge used in this study indicates that the erosion process was more energy demanding and the erosion process was less shear dependent for the activated sludge used in this study.     

Effects of hourly load variation on treatment characteristics in anaerobic-aerobic activated sludge process

The effect of hourly load change on the treatment characteristics in an anaerobic-aerobic activated sludge process was compared for two types of variation. When the variation of wastewater concentration or flow rate was applied to the treatment unit according to normal distribution function like effluent pattern in actual life, the treatment system gave relatively stable and successful removal of nitrogen and phosphorus compounds. When the mass flow rate of nitrogen applied to the treatment unit was equal, the performance of the present process was almost same regardless of load variation mode. The simulation of treatment behavior was carried out successfully by using the kinetic equations for sludge floc and the reactor models which considered the treatment unit as a completely mixed tank.     

Treatment of a combined dairy and domestic wastewater in an up-flow anaerobic sludge blanket (UASB) reactor followed by activated sludge (AS system)

The feasibility of using an up-flow anaerobic sludge blanket (UASB) reactor followed by activated sludge (AS system) for the treatment of wastewater discharged from dairy factory was explored. The UASB reactor was operated at a hydraulic retention time (HRT) of 24 h and organic loading rates (OLRs) ranging from 1.9 to 4.4 kgCOD/m³.d. The average total chemical oxygen demand (COD_total) and total biological oxygen demand (BOD_5total) concentrations of the UASB reactor effluent were 1385 and 576 mg/l, corresponding to percentage removal of 69% and 79%, respectively. Total suspended solids (TSS) and volatile suspended solids (VSS) removal averaged above 72% and 75%, respectively. Residual phosphorous and oil and grease concentrations of the UASB reactor effluent were 8.2 and 44 mg/l, corresponding to percentage removal values of 63% and 83%, respectively. This good performance could be attributed to the relatively long sludge residence time (SRT = 76 d) imposed to the reactor. Total and faecal coliform counts were reduced in the treated effluent by a value of 1.07 and 0.9 log₁₀, respectively. The net sludge yield coefficient was found to be 0.2 g VSS per g COD_total removed per day, corresponding to 20% of the total influent COD imposed to the UASB reactor. The volatile solids / total solids (VS/TS) ratio of 0.66 of excess sludge revealed its good quality. Preliminary batch experiments of the AS system treating UASB reactor effluent indicated first-order removal kinetics between total organic carbon (TOC) and contact time. The TOC removal reached 80%, resulting in only 47 mg/l in the final effluent at a HRT of 2.0 h. Accordingly, the AS system was operated at a HRT of 2.0 h. The system achieved a substantial reduction of COD_total, BOD_{5 total}, TSS and oil and grease resulting effluent quality with residual values of only 35.0, 7.0, 14.0 and 2.8 mg/l, respectively. The geometric mean of total and faecal coliform counts was reduced by a value of 1.28 and 1.64 log₁₀, respectively. Based on these results, it is recommended to use of an integrated system consisting of a UASB reactor followed by the AS system for the treatment of a combined dairy and domestic wastewater to produce a good effluent quality complying with the standards for discharge into agricultural drains.     

Solution of the population balance equation using the sectional quadrature method of moments (SQMOM)

A discrete framework is introduced for simulating the particulate physical systems governed by population balance equations (PBE) with particle splitting (breakage) and aggregation based on accurately conserving (from theoretical point of view) an unlimited number of moments associated with the particle size distribution. The basic idea is based on the concept of primary and secondary particles, where the former is responsible for distribution reconstruction while the latter is responsible for different particle interactions such as splitting and aggregation. The method is found to track accurately any set of low-order moments with the ability to reconstruct the shape of the distribution. The method is given the name: the sectional quadrature method of moments (SQMOM) and has the advantage of being not tied to the inversion of large sized moment problems as required by the classical quadrature method of moments (QMOM). These methods become ill conditioned when a large number of moments are needed to increase their accuracy. On the contrary, the accuracy of the SQMOM increases by increasing the number of primary particles while using fixed number of secondary particles. Since the positions and local distributions for two secondary particles are found to have an analytical solution, no large moment inversion problems are anymore encountered. The generality of the SQMOM is proved by showing that all the related sectional and quadrature methods appearing in the literature for solving the PBE are merely special cases. The method has already been extended to bivariate PBEs.     

Simulation of crystal size and shape by means of a reduced two-dimensional population balance model

Commonly, population balance modeling for crystallization processes only considers one inner variable. Usually, a variable characterizing particle size, like a sphere-equivalent diameter is employed. However, crystal structures are obviously not spherical but exhibit a complex habit. Often, the habit is even crucial for the quality of the product or for the operability of downstream filter units. To describe the transient behavior of crystals in a batch process considering two-dimensional growth and nucleation, a multidimensional population balance needs to be employed. Considering two characteristic lengths of a crystal, the standard discretization of such a system (by, e.g. finite differences) leads to quite a large model size, which may be unsuited for model-based control and parameter identification purposes. In this contribution a model reduction which is based on two steps is proposed. First, a coordinate transformation is performed to model the system not in terms of two characteristic lengths but by means of the crystal volume and a shape factor. In a second step the actual model reduction is performed by generating cross-moments for the two-dimensional representation. An ansatz for the two-dimensional crystal size distribution, which gives full flexibility in the volume coordinate but restricts the dependence in the shape factor κ, allows the closure of the system of moments. The reduced system consists of three coupled population balance equations in which all three are structurally similar to a single one-dimensional population balance equation, where growth and nucleation only are considered. Solving this reduced system allows the detailed simulation of the easily measurable volume-based number density distribution and preserves average and dispersity information on the crystal shape. The resulting model size, however, scales only linearly with the number of discretization grid points instead of the quadratic scaling for standard discretizations. Numerical results for the crystallization of potassium dihydrogen phosphate (KH₂PO₄) in a batch process are presented for illustration.     

Modeling and simulation of mixing in water-in-oil emulsion flow through a valve-like element using a population balance model

Emulsion flows are very common in natural processes as well as in several engineering areas, such as in the process of desalting crude oil that occurs in refineries. This kind of flow is described as a polydispersed multiphase flow. In this work, we evaluated the behavior of water-in-oil emulsion flowing through a duct with an element used to mimic the effect of a globe valve. An Eulerian multi-fluid approach was employed by solving the population balance equation coupled with computational fluid dynamics. Coalescence and breakage models recently developed were extended to this inhomogeneous model. A bivariate population balance problem was also solved to demonstrate the mixing caused by the valve-like element. The simulated results showed good agreement with the available experimental data for the Sauter and DeBroukere mean diameters.     

Investigation of soot formation in turbulent flames with a pseudo-bivariate population balance model

Soot inception and subsequent aggregation, surface growth and oxidation are described through a new pseudo-bivariate population balance model solved with the direct quadrature method of moments (DQMOM) and implemented in a commercial computational fluid dynamics (CFD) code. This modelling strategy, that in this work is presented in its Reynolds-averaged Navier-Stokes (RANS) equation formulation, has the advantage, over conventional approaches based on the solution of a single transport equation for the soot volume fraction, to overcome the assumption of mono-dispersed soot particle size distribution. On the contrary the pseudo-bivariate approach presented in this work is able to represent the evolution of the soot particle size distribution with good accuracy and affordable computational costs, especially when compared with other multi-variate formulations previously developed. This new pseudo-bivariate model is firstly formulated and presented, then predictions obtained with different soot inception models are compared with some recent experimental data from the literature and the role played by the different phenomena involved (e.g., turbulence, oxidation and radiation) is investigated.     

Understanding the role of restructuring in flocculation: The application of a population balance model

The effect of shear on floc properties was observed through population balance to comprehend the mechanisms of flocculation, in particular the role of restructuring. Little fundamental attention has been given before to the shear influence responsible for creating compact aggregates, while the floc characteristics might differ in other conditions. It is crucial to understand how aggregates evolve to steady state, if their properties are to be ‘tailored’ to suit subsequent solid-liquid separation. From a previous experimental study (Langmuir 18(6) (2002) 1974), restructuring was observed to occur extensively in the flocculation of latex particles in couette-flow, and was proposed to be responsible for the decrease in floc size on their transition to equilibrium. On the other hand, flocs of larger primary particles were more susceptible to breakage, with densification occurring as a result of fragmentation and re-aggregation. Denser flocs were found when structural deformation dominated, particularly in the initial stage of the process, while comparatively tenuous ones were observed when formation and breakage kinetics were the governing mechanisms. The distinct manners in which aggregates of different primary particle sizes evolved with time, were replicated with a population balance that incorporated the floc structural variation; verifying that restructuring indeed played a crucial role under certain flocculation conditions.