Dynamic Mass Balance Research Articles

Coastal eutrophication: Whether N and/or P should be abated depends on the dynamic mass balance

Whether nitrogen (N) and/or phosphorus (P) should be abated to counteract coastal eutrophication remains controversial. System-wide lake experiments presented in PNAS have shown that P control was essential for dampening algal blooms whereas N control only strengthened the competitive advantage of cyanobacteria and increased fixation of dissolved N2 from the atmosphere (1 …

A dynamic model for the global cycling of anthropogenic vanadium

Vanadium is a major trace metal in fossil fuels. Combustion of residual fuel oils and coal in industrialized economies is recognized as the major source of anthropogenic vanadium. A dynamic mass balance model assessed the influence of anthropogenic inputs on the global distribution and cycling of vanadium between 1700 and 2400 assuming different fossil fuel consumption and V production (mining) scenarios. Anthropogenic V sources were divided into fossil fuel combustion, industrial, and domestic (nonindustrial human activity). By 2050, inputs of anthropogenic V could comprise ≈75–85% of those to the atmosphere, ≈21–33% to ocean dissolved, ≈9–13% to ocean particulate, and ≈28–43% of inputs to land; with between ≈61–64% of all anthropogenic inputs attributable to fossil fuel combustion. Contributions from combustion and industrial sources, although dominant relative to contributions from domestic sources between 1900 and 2100, were estimated to peak between 2000 and 2050. Accumulation of anthropogenic V on land and in the ocean apparently occurs because natural removal processes are unable to cope with increasing amounts and rates of anthropogenic contributions. Impacts or hazards associated with anthropogenic inputs are unlikely to be discernible or significant on a global scale, but may be measurable and meaningful at smaller scales (coastal waters, continental shelves, and bays), in the locality of specific sources, or given an unfavorable exposure scenario.

Quantitative modeling of triacylglycerol homeostasis in yeast – metabolic requirement for lipolysis to promote membrane lipid synthesis and cellular growth

Triacylglycerol metabolism in Saccharomyces cerevisiae was analyzed quantitatively using a systems biological approach. Cellular growth, glucose uptake and ethanol secretion were measured as a function of time and used as input for a dynamic flux-balance model. By combining dynamic mass balances for key metabolites with a detailed steady-state analysis, we trained a model network and simulated the time-dependent degradation of cellular triacylglycerol and its interaction with fatty acid and membrane lipid synthesis. This approach described precisely, both qualitatively and quantitatively, the time evolution of various key metabolites in a consistent and self-contained manner, and the predictions were found to be in excellent agreement with experimental data. We showed that, during pre-logarithmic growth, lipolysis of triacylglycerol allows for the rapid synthesis of membrane lipids, whereas de novo fatty acid synthesis plays only a minor role during this growth phase. Progress in triacylglycerol hydrolysis directly correlates with an increase in cell size, demonstrating the importance of lipolysis for supporting efficient growth initiation.

Metabolic Dynamics in Skeletal Muscle during Acute Reduction in Blood Flow and Oxygen Supply to Mitochondria: In-Silico Studies Using a Multi-Scale, Top-Down Integrated Model

Control mechanisms of cellular metabolism and energetics in skeletal muscle that may become evident in response to physiological stresses such as reduction in blood flow and oxygen supply to mitochondria can be quantitatively understood using a multi-scale computational model. The analysis of dynamic responses from such a model can provide insights into mechanisms of metabolic regulation that may not be evident from experimental studies. For the purpose, a physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics was developed to describe dynamic responses of key chemical species and reaction fluxes to muscle ischemia. The model, which incorporates key transport and metabolic processes and subcellular compartmentalization, is based on dynamic mass balances of 30 chemical species in both capillary blood and tissue cells (cytosol and mitochondria) domains. The reaction fluxes in cytosol and mitochondria are expressed in terms of a general phenomenological Michaelis-Menten equation involving the compartmentalized energy controller ratios ATP/ADP and NADH/NAD+. The unknown transport and reaction parameters in the model are estimated simultaneously by minimizing the differences between available in vivo experimental data on muscle ischemia and corresponding model outputs in coupled with the resting linear flux balance constraints using a robust, nonlinear, constrained-based, reduced gradient optimization algorithm. With the optimal parameter values, the model is able to simulate dynamic responses to reduced blood flow and oxygen supply to mitochondria associated with muscle ischemia of several key metabolite concentrations and metabolic fluxes in the subcellular cytosolic and mitochondrial compartments, some that can be measured and others that can not be measured with the current experimental techniques. The model can be applied to test complex hypotheses involving dynamic regulation of cellular metabolism and energetics in skeletal muscle during physiological stresses such as ischemia, hypoxia, and exercise.

A Model for the Presence of Polychlorinated Biphenyls (PCBs) in the Willamette River Basin (Oregon)

The Willamette River drains a 32,000 km2 basin (Basin) in northwestern Oregon. Owing to their persistence and toxicity, polychlorinated biphenyls (PCBs) in resident fish within the Basin at levels above consumption advisory thresholds are a human and environmental health concern. This concern may trigger a Willamette River Total Maximum Daily Load (TMDL) for PCBs, at which time both their probable sources and the mechanism by which they came to be distributed throughout the Basin will be of considerable regulatory interest. Deposition within the Basin of some portion of global primary (1930-1980) and secondary (post-1980) emissions arriving via long-range advective transport in the atmosphere was posited as an explanation. This proposition was explored with a seasonally responsive, dynamic mass balance watershed-scale model that estimated concentrations of toxicologically relevant congeners (PCB-077, -118, -169) in various environmental media over a 90-year period, assuming advective inflow to the Basin's atmosphere to be the only PCB congener source. Model results suggest that rising air concentrations, and associated advective inflows, from increasing primary emissions between 1930 and 1975 (PCB-118 peak inflow, 1970, approximately equal to 11 kg y(-1)) and declining primary and secondary emissionsthereafter, could have yielded congener concentrations observed in air, soil, and fish between 1993 and 2003. The possibility that observed concentrations may be obtainable entirely with inputs from global legacy sources raises questions as to the efficacy of a TMDL directed primarily at local point or area sources. Better characterization of potential sources, and collection of additional soil and air data combined with more sophisticated modeling, appear to be necessary precursors to any PCB TMDL for the Willamette River.

Dynamic spatially explicit mass-balance modeling for targeted watershed phosphorus management: I. Model development

Surface waters are frequently impaired by excessive phosphorus (P) from nonpoint sources, especially in regions of intensive livestock agriculture. Despite concerted efforts to apply new management measures, reductions in nonpoint source P loads have been difficult to accomplish. Watershed management to reduce P export could be more cost-effective if treatments were targeted to critical source areas at high risk for excessive P export. These critical source areas can be defined as the intersection of P source areas and active runoff contributing areas; such areas vary in space and time due to watershed characteristics and management practices. We developed an approach to identify, analyze, and map high-risk areas for P export by integrating spatial data with land use and agronomic data. We evaluated changes over time and space in soil P concentration and P export in response to changes in inputs and outputs with a dynamic mass-balance simulation model running in grid cells across a watershed. The temporal and spatial relationships that define the risk of P export are captured simultaneously using a raster-based distributed dynamic modeling approach and related to management interventions. Simulated responses to management interventions are analyzed and displayed spatially through a geographic information system (GIS). This approach allows the spatial distribution of P runoff risk to be tracked through time in response to long-term P input/output balance, evolving from either continuation of current practices or from management changes specifically targeted to areas of high P loss risk. Baseline simulations show that if present-day management continues, both soil test P and P export will increase dramatically in some parts of a test watershed; critical P source areas in a watershed will evolve over time and are likely to occur in limited areas that can be identified and tracked. Model results can contribute to improved targeting of scarce resources by focusing management interventions on those areas at highest risk of nutrient loss. This paper describes the underlying principles of the model, discusses the process of model development, and presents the final modeling system. Application of the model to alternative management scenarios is discussed in a subsequent paper.

MAM-An Aquivalence-based Dynamic Mass Balance Model for the Fate of Non-Volatile Organic Chemicals in the Agricultural Environment

A Multimedia Agricultural Model (MAM) for predicting the fate and transport of Non- Volatile Organic Chemicals (NVOCs) in the agricultural environment was presented. It is an expanded and modified version of the three compartmental model introduced by Batiha and co-authors in 2007, which is an aquivalence-based level IV. MAM considered five environmental compartments to include the air, water, soil, sediment and vegetation. It calculates the complete steady-state mass budgets for the air, water and particulate organic carbon between the model compartments. MAM compartments were connected by advective and intermedia transport processes. Degradation can take place in every compartment. The mass balances for each of the compartments result in a system of five differential equations, solved numerically to yield estimates of concentrations, masses, transport fluxes and reaction rates as a function of time. All the equations required for MAM calculations were provided.

Modeling Cellular Metabolism and Energetics in Skeletal Muscle: Large-Scale Parameter Estimation and Sensitivity Analysis

Skeletal muscle plays a major role in the regulation of whole-body energy metabolism during physiological stresses such as ischemia, hypoxia, and exercise. Current experimental techniques provide relatively little in vivo data on dynamic responses of metabolite concentrations and metabolic fluxes in skeletal muscle to such physiological stimuli. As a complementary approach to experimental measurements and as a framework for quantitatively analyzing available in vivo data, a physiologically based model of skeletal muscle cellular metabolism and energetics is developed. This model, which incorporates key transport and reaction processes, is based on dynamic mass balances of 30 chemical species in capillary (blood) and tissue (cell) domains. The reaction fluxes in the cellular domain are expressed in terms of a generalized Michaelis?Menten equation involving energy controller ratios ATP/ADP and ATP/ADP and NADH/NAD+ . This formalism introduces a large number of unknown parameters ( approximately 90). Estimating these parameters from in vivo sparse data and evaluating dynamic sensitivities of the model outputs with respect to these parameters is a challenging problem. Parameter estimation is accomplished using an efficient, nonlinear, constraint-based, optimization algorithm that minimizes differences between available experimental data and corresponding model outputs by explicitly utilizing equality constraints on resting fluxes and concentrations. With the estimated parameter values, the model is able to simulate dynamic responses to reduced blood flow (ischemia) of key metabolite concentrations and metabolic fluxes, both measured and nonmeasured. A general parameter sensitivity analysis is carried out to determine and characterize the parameters having the most and least effects on the measured outputs.

The Role of Ca2+ in Coupling Cardiac Metabolism with Regulation of Contraction

The heart adapts the rate of mitochondrial ATP production to energy demand without noticeable changes in the concentration of ATP, ADP and Pi, even for large transitions between different workloads. We suggest that the changes in demand modulate the cytosolic Ca2+ concentration that changes mitochondrial Ca2+ to regulate ATP production. Thus, the rate of ATP production by the mitochondria is coupled to the rate of ATP consumption by the sarcomere cross-bridges (XBs). An integrated model was developed to couple cardiac metabolism and mitochondrial ATP production with the regulation of Ca2+ transient and ATP consumption by the sarcomere. The model includes two interrelated systems that run simultaneously utilizing two different integration steps: (1) The faster system describes the control of excitation contraction coupling with fast cytosolic Ca2+ transients, twitch mechanical contractions, and associated fluctuations in the mitochondrial Ca2+. (2) A slower system simulates the metabolic system, which consists of three different compartments: blood, cytosol, and mitochondria. The basic elements of the model are dynamic mass balances in the different compartments. Cytosolic Ca2+ handling is determined by four organelles: sarcolemmal Ca2+ influx and efflux; sarcoplasmic reticulum (SR) Ca2+ release and sequestration (SR); binding and dissociation from sarcomeric regulatory troponin complexes; and mitochondrial Ca2+ flows. Mitochondrial Ca2+ flows are determined by the Ca2+ uniporter and the mitochondrial Na+Ca2+ exchanger. The cytosolic Ca2+ determines the rate of ATP consumption by the sarcomere. Ca2+ binding to troponin regulates the rate of XBs recruitment and force development. The mitochondrial Ca2+ concentration determines the pyruvate dehydrogenase activity and the rate of ATP production by the F(1)-F(0) ATPase. The workload modulates the cytosolic Ca2+ concentration through feedback loops. The preload and afterload affect the number of strong XBs. The number of strong XBs determines the affinity of troponin for Ca2+, which alters the cytosolic Ca2+ transient. Model simulations quantify the role of Ca2+ in simultaneously controlling the power of contraction and the rate of ATP production. It explains the established empirical observation that significant changes in the metabolic fluxes can occur without significant changes in the key nucleotide (ATP and ADP) concentrations. Quantitative investigations of the mechanisms underlying the cardiac control of biochemical to mechanical energy conversion may lead to novel therapeutic modalities for the ischemic and failing myocardium.

Development of a simulation for teaching fluid therapy

The course “Management of Fluid and Electrolyte Disorders” is taught using lectures and paper‐based case scenarios. While the latter provide an excellent basis for application of basic‐science concepts, they lack key components of genuine clinical cases that, by nature, are diverse, change over time, and respond in unique ways to therapeutic intervention. We developed a dynamic mathematical model using STELLA® software that simulates normal and abnormal fluid and electrolyte balance in the dog. The simulation outputs real‐time clinical data allowing students to develop a therapeutic plan based on their clinical assessment. Students administer fluids and supplements and the model responds in real‐time, requiring regular reassessment and intervention. Level of success is determined by clinical outcome including improvement, deterioration, or death. Underlying variables can be exploited to illustrate and apply concepts such as compartment volumes, endocrine responses, and dynamic mass balance. We expect that the simulation will allow students to improve clinical competency, apply fundamental principles in disparate contexts, and practice the “art” of fluid therapy without use of live animals.

Model-based determination of hydrogen system emissions of motor vehicles using climate-chamber test facilities

Because of air quality problems, the problem of CO 2 related greenhouse gas emissions and shortage of fossil fuels, many vehicles with gaseous fuels (CNG, biogas, hydrogen, etc.) are under research and development. Such vehicles have to prove that both their exhaust emissions and their overall system emissions (including running loss) remain below certain safety limits before they can be used in practice. This paper presents a cost-effective way of monitoring such system emissions from hydrogen or other gaseous fuel powered vehicles within an air-conditioned chassis dynamometer test cell, as commonly used for low ambient emission tests on gasoline vehicles. The only additional equipment needed is a low-concentration sensor for the gas of interest (e.g. hydrogen). The method is based on concentration measurements and a dynamic mass balance model. It is shown by a real experiment that very low emissions can be recorded. Additionally, error bounds and sensitivities on different parameters such as air exchange ratio are quantified.

A Dynamic Mass-balance Model for Phosphorus in Lakes with a Focus on Criteria for Applicability and Boundary Conditions

This paper presents an improved version of a general, process-based mass-balance model (LakeMab/LEEDS) for phosphorus in entire lakes (the ecosystem scale). The focus in this work is set on the boundary conditions, i.e., the domain of the model, and critical tests to reveal those boundary conditions using data from a wide limnological range. The basic structure of the model, and many key equations have been presented and motivated before, but this work presents several new developments. The LakeMab-model is based on ordinary differential equations regulating inflow, outflow and internal fluxes and the temporal resolution is one month to reflect seasonal variations. The model consists of four compartments: surface water, deep water, sediment on accumulation areas and sediment on areas of erosion and transportation. The separation between the surface-water layer and the deep-water layer is not done from water temperature data, but from sedimentological criteria (from the theoretical wave base, which regulates where wind/wave-induced resuspension of fine sediments occurs). There are algorithms for processes regulating internal fluxes and internal loading, e.g., sedimentation, resuspension, diffusion, mixing and burial. Critical model tests were made using data from 41 lakes of very different character and the results show that the model could predict mean monthly TP-concentrations in water very well (generally within the uncertainty bands given by the empirical data). The model is even easier to apply than the well-known OECD and Vollenweider models due to more easily accessed driving variables.

Numerical Spray Model of the Fluidized Bed Coating Process

In this study, a new model for the batch top-spray fluidized bed coating process is presented. The model is based on the one-dimensional (axial) discretization of the bed volume into different control volumes, in which the dynamic heat and mass balances for air, water vapor, droplets, core particles, and coating material were established. The coupling of the droplet phase's mass and heat transfer terms with the gas and solid phases was established by means of a droplet submodel in which droplet trajectories were individually simulated. The model calculation method combines a Monte Carlo technique for the simulation of the particle exchange with the first-order Euler's method for solving the heat and mass balances, enabling the prediction of both the dynamic coating mass distribution and the one-dimensional (axial) thermodynamic behavior of the fluidized bed during batch operation. The simulation results were validated using experimental two-dimensional spatial air temperature and air humidity distributions, which were measured in a fluidized bed pilot reactor using a scanning probe. Sensitivity analysis was carried out to study the effect of controllable process variables, such as fluidization air and atomization air properties, as well as the properties of the spraying liquid upon the simulated dynamic temperature and humidity distributions. Also, the effects of relevant process variables on growth rate uniformity and process yield were studied. Based on these sensitivity studies it was concluded that nozzle parameters, such as air pressure and positioning with respect to the bed, are as important as the fluidization air properties (humidity, temperature, and flow rate) for the coating growth rate uniformity and process yield.

Development of a multi-scale, multi-phase, multi-zone dynamic model for the prediction of particle segregation in catalytic olefin polymerization FBRs

A comprehensive multi-scale, multi-phase, multi-compartment dynamic model is developed to analyze the extent of particle segregation in catalytic, gas-phase ethylene–propylene copolymerization fluidized bed reactors (FBRs). From the numerical solution of the proposed integrated model, the temporal-spatial evolution of the morphological (i.e., particle size distribution, PSD) and molecular (i.e., molecular weight distribution, MWD) polymer properties in a catalytic polymerization FBR can be predicted. In particular, the polymer molecular properties are determined by employing a generalized multi-site, Ziegler–Natta kinetic scheme. To determine the growth of a single catalyst/polymer particle, the random pore polymeric flow model (RPPFM) is utilized. The RPPFM is solved together with a dynamic discretized particle population balance equation (PBE) to calculate the dynamic evolution of PSD in the various compartments of the FBR. Moreover, overall dynamic mass and energy balances are derived in order to assess the dynamic behavior of catalytic gas-phase FBRs. The effects of various fluidized bed operating conditions (e.g., fluidization gas velocity, temperature and catalyst feed rate) on the morphological and molecular distributed polymer properties are thoroughly analyzed.

Model of oxygen transport and metabolism predicts effect of hyperoxia on canine muscle oxygen uptake dynamics

Previous studies have shown that increased oxygen delivery, via increased convection or arterial oxygen content, does not speed the dynamics of oxygen uptake, Vo(2m), in dog muscle electrically stimulated at a submaximal metabolic rate. However, the dynamics of transport and metabolic processes that occur within working muscle in situ is typically unavailable in this experimental setting. To investigate factors affecting Vo(2m) dynamics at contraction onset, we combined dynamic experimental data across working muscle with a mechanistic model of oxygen transport and metabolism in muscle. The model is based on dynamic mass balances for O(2), ATP, and PCr. Model equations account for changes in cellular ATPase, oxidative phosphorylation, and creatine kinase fluxes in skeletal muscle during exercise, and cellular respiration depends on [ADP] and [O(2)]. Model simulations were conducted at different levels of arterial oxygen content and blood flow to quantify the effects of convection and diffusion of oxygen on the regulation of cellular respiration during step transitions from rest to isometric contraction in dog gastrocnemius muscle. Simulations of arteriovenous O(2) differences and (.)Vo(2m) dynamics were successfully compared with experimental data (Grassi B, Gladden LB, Samaja M, Stary CM, Hogan MC. J Appl Physiol 85: 1394-1403, 1998; and Grassi B, Gladden LB, Stary CM, Wagner PD, Hogan MC. J Appl Physiol 85: 1404-1412, 1998), thus demonstrating the validity of the model, as well as its predictive capability. The main findings of this study are: 1) the estimated dynamic response of oxygen utilization at contraction onset in muscle is faster than that of oxygen uptake; and 2) hyperoxia does not accelerate the dynamics of diffusion and consequently muscle oxygen uptake at contraction onset due to the hyperoxia-induced increase in oxygen stores. These in silico derived results cannot be obtained from experimental observations alone.

Estimation of metabolic fluxes, expression levels and metabolite dynamics of a secondary metabolic pathway in potato using label pulse‐feeding experiments combined with kinetic network modelling and simulation

In this paper we present a method that allows dynamic flux analysis without a priori kinetic knowledge. This method was developed and validated using the pulse-feeding experimental data obtained in our previous study (Matsuda et al., 2005), in which incorporation of exogenously applied l-phenylalanine-d(5) into seven phenylpropanoid metabolites in potato tubers was determined. After identification of the topology of the metabolic network of these biosynthetic pathways, the system was described by dynamic mass balances in combination with power-law kinetics. After the first simulations, some reactions were removed from the network because they were not contributing significantly to network behaviour. As a next step, the exponents of the power-law kinetics were identified and then kept at fixed values during further analysis. The model was tested for statistical reliability using Monte Carlo simulations. Most fluxes could be identified with high accuracy. The two test cases, control and after elicitation, were clearly distinguished, and with elicitation fluxes to N-p-coumaroyloctopamine (pCO) and N-p-coumaroyltyramine (pCT) increased significantly, whereas those for chlorogenic acid (CGA) and p-coumaroylshikimate decreased significantly. According to the model, increases in the first two fluxes were caused by induction/derepression mechanisms. The decreases in the latter two fluxes were caused by decreased concentrations of their substrates, which in turn were caused by increased activity of the pCO- and pCT-producing enzymes. Flux-control analysis showed that, in most cases, flux control was changed after application of elicitor. Thus the results revealed potential targets for improving actions against tissue wounding and pathogen attack.

Modelling the effects of Po River discharge, internal nutrient cycling and hydrodynamics on biogeochemistry of the Northern Adriatic Sea

This study investigates the coupling of physical and biological processes in the Northern Adriatic Sea through use of a dynamic mass balance approach derived from an interdisciplinary model of hydrodynamics and water quality. Emphasis is placed on modelling the role of nutrient inputs from the Po River and the response of phytoplankton concentrations and distributions, and basin-wide nutrient fluxes. The effects of riverine inflows, seasonal stratification and meteorological forcing were assessed with a dynamically coupled 3D hydrodynamic (ELCOM) and ecological (CAEDYM) model after validation with in situ field and remote sensing data. Model simulation results and mass balance calculations indicate a close coupling of physical and biological processes over a range of space and time scales. Comparison of fluxes from advection and particulate organic matter sedimentation indicate that nutrient and phytoplankton levels of the Northern Adriatic Sea are sensitive to variations in riverine nutrient loadings. A net total phosphorus accumulation of 4.61 × 10 6 kg was determined for the basin in 2002, with different climate scenarios and riverine nutrient loadings resulting in varied system responses reflected in this net TP accumulation. Changes in net accumulation of nutrients are considerably lower than variations in nutrient loadings, which suggests that the Northern Adriatic has substantial buffering capacity.

Multi-Scale Computational Model of Fuel Homeostasis During Exercise: Effect of Hormonal Control

A mathematical model of the whole-body metabolism is developed to predict fuel homeostasis during exercise by using hormonal control over cellular metabolic processes. The whole body model is composed of seven tissue compartments: brain, heart, liver, GI (gastrointestinal) tract, skeletal muscle, adipose tissue, and "other tissues". Each tissue compartment is described by dynamic mass balances and major cellular metabolic reactions. The glucagon-insulin controller is incorporated into the whole body model to predict hormonal changes during exercise. Moderate [150 W power output at 60% of peak oxygen consumption (VO(2max))] exercise for 60 min was implemented by increasing ATP utilization rates in heart and skeletal muscle. Arterial epinephrine level was given as an input function, which directly affects heart and skeletal muscle metabolism and indirectly other tissues via glucagon-insulin controller. Model simulations were validated with experimental data from human exercise studies. The exercise induced changes in hormonal signals modulated metabolic flux rates of different tissues in a coordinated way to achieve glucose homeostasis, demonstrating the efficacy of hormonal control over cellular metabolic processes. From experimental measurements of whole body glucose balance and arterial substrate concentrations, this model could predict the dynamic changes of hepatic glycogenolysis and gluconeogenesis, which are not easy to measure experimentally, suggesting the higher contribution of glycogenolysis ( approximately 75%). In addition, it could provide dynamic information on the relative contribution of carbohydrates and lipids for fuel oxidation in skeletal muscle. Model simulations indicate that external fuel supplies from other tissue/organ systems to skeletal muscle become important for prolonged exercise emphasizing the significance of interaction among tissues. In conclusion, this model can be used as a valuable complement to experimental studies due to its ability to predict what is difficult to measure directly, and usefulness to provide information about dynamic behaviors.

A dynamic mass balance model for phosphorus fluxes and concentrations in coastal areas

AbstractThis paper presents a general, process‐based mass balance model (CoastMab) for total phosphorus (TP) in defined coastal areas (at the ecosystem scale). The model is based on ordinary differential equations and calculates inflow, outflow and internal fluxes on a monthly basis. It consists of four compartments: surface water, deep water, erosion/transportation areas for fine sediments and accumulation areas for fine sediments. The separation between surface water and deep water is not done based on water temperature, but on sedimentological criteria instead (from the theoretical wave base). There are algorithms for all major internal TP fluxes (sedimentation, resuspension, diffusion, mixing and burial). Validations were performed using data from 21 different Baltic coastal areas. The results show that the model predicts monthly TP in water and chlorophyll a very well (generally within the uncertainty bands of the empirical data). The model has also been put through sensitivity tests, which show that the most important factor regulating the predictions of the model is generally the TP concentration in the sea beyond the coast. The model is simple to apply, since all driving variables may be accessed from maps or monitoring programs. The driving variables include coastal area, section area (between the defined coastal area and the adjacent sea), mean and maximum depths, latitude (used to predict water temperatures, stratification and mixing), salinity and TP concentration in the sea. Many of the model structures are general and could be used for areas other than those included in this study, e.g., for open coasts, estuaries or tidal coasts, as well as for other substances than phosphorus.

Separation of para-xylene from xylene mixture via crystallization

Crystallization kinetics of para-xylene from xylene isomers mixture using a lab-scale cooling batch crystallizer were determined. The cooling batch crystallizer type is simple, flexible and requires less process development. Dynamic mass and population balances were used to model the batch crystallizer. The model equations were solved using the numerical method of lines; a new proposed solution method. The kinetic parameters of nucleation and growth rates were estimated by measuring the concentration and the total mass of para-xylene suspended crystals during the process time. A nonlinear optimization technique was then applied to estimate the parameters. The effect of the cooling strategy on the estimated parameters was studied. It was found that model predictions using the optimum estimated parameters were in good agreement with the experimental results under various cooling strategies. The optimal kinetic parameters were then used to find the optimum cooling strategy to maximize the yield of para-xylene crystals which have an average size greater than 0.5 mm. A new objective function was formulated and also, a nonlinear optimization technique was applied to find the optimum cooling strategy to achieve this product characterization. The optimization technique converged successfully and the proposed objective function was found to be effective to optimize the para-xylene crystallization process.