Anaerobic digestion model no. 1-based distributed parameter model of an anaerobic reactor: I. Model development

This work presents a distributed parameter model of the anaerobic digestion process. The model is based on the Anaerobic digestion model no. 1 (ADM1) and was developed to simulate anaerobic digestion process in high-rate reactors with significant axial dispersion, such as in upflow anaerobic sludge bed (UASB) reactors. The model, which was named ADM1d, combines ADM1's kinetics of biomass growth and substrate transformation with axial dispersion material balances. ADM1d uses a hyperbolic tangent function to describe biomass distribution within a one compartment model. A comparison of this approach with a two-compartment, sludge bed - liquid above the bed, model showed similar simulation results while the one-compartment model had less equations. A comparison of orthogonal collocation and finite difference algorithms for numerical solution of ADM1d showed better stability of the finite difference algorithm.     

Estimation of kinetic parameters in a structured yeast model using regularisation.

In this work, a procedure for estimating kinetic parameters in biochemically structured models was developed. The approach is applicable when the structure of a kinetic model has been set up and the kinetic parameters should be estimated. The procedure consists of five steps. First, initial values were found in or calculated from literature. Hereafter using sensitivity analysis the most sensitive parameters were identified. In the third step physiological knowledge was combined with the parameter sensitivities to manually tune the most sensitive parameters. In step four, a global optimisation routine was applied for simultaneous estimation of the most sensitive parameters identified during the sensitivity analysis. Regularisation was included in the simultaneous estimation to reduce the effect of insensitive parameters. Finally, confidence intervals for the estimated parameters were calculated. This parameter estimation approach was demonstrated on a biochemically structured yeast model containing 11 reactions and 37 kinetic constants as a case study.     

An original procedure for physical simulation of upflow anaerobic sludge blanket reactors

A procedure for sludge blanket reactors physical simulation is presented. To simulate the liquid phase, a solution of 1.0 g/l of polyvinyl alcohol provided the desired rheological behavior. Biological granules presented in UASB reactors were simulated using granules of a water absorbent acrylic polymer capable to expand up to one hundred times in volume when moistened. The biochemical reactions that produces methane and carbon dioxide in anaerobic reactors were simulated reacting nitric acid and sodium bicarbonate. This procedure differs from gas injection since the gas is produced at the reactor core as it happens in the actual situation, thus the simulation is more realistic. Flow visualization and residence time distribution measurements were used to verify if the proposed procedure acceptably simulates UASB reactors treating wastewater. All tests were performed in a 10.5 l bench scale reactor and the results allow to recommend this method whenever flow visualization and reactor physical simulation are useful for reactor design and development.     

Identifyability measures to select the parameters to be estimated in a solid‐state fermentation distributed parameter model

Process modeling can lead to of advantages such as helping in process control, reducing process costs and product quality improvement. This work proposes a solid‐state fermentation distributed parameter model composed by seven differential equations with seventeen parameters to represent the process. Also, parameters estimation with a parameters identifyability analysis (PIA) is performed to build an accurate model with optimum parameters. Statistical tests were made to verify the model accuracy with the estimated parameters considering different assumptions. The results have shown that the model assuming substrate inhibition better represents the process. It was also shown that eight from the seventeen original model parameters were nonidentifiable and better results were obtained with the removal of these parameters from the estimation procedure. Therefore, PIA can be useful to estimation procedure, since it may reduce the number of parameters that can be evaluated. Further, PIA improved the model results, showing to be an important procedure to be taken. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:905–917, 2016     

Controlled shear affinity filtration (CSAF): a new technology for integration of cell separation and protein isolation from mammalian cell cultures

Up-flow anaerobic sludge blanket (UASB) reactors are being used with increasing regularity all over the world, especially in India, for a variety of wastewater treatment operations. Consequently, there is a need to develop methodologies enabling one to determine UASB reactor performance, not only for designing more efficient UASB reactors but also for predicting the performance of existing reactors under various conditions of influent wastewater flows and characteristics. This work explores the feasibility of application of an artificial neural network-based model for simulating the performance of an existing UASB reactor. Accordingly, a neural network model was designed and trained to predict the steady-state performance of a UASB reactor treating high-strength (unrefined sugar based) wastewater. The model inputs were organic loading rate, hydraulic retention time, and influent bicarbonate alkalinity. The output variables were one or more of the following, effluent substrate concentration (Se), reactor bicarbonate alkalinity, reactor pH, reactor volatile fatty acid concentration, average gas production rate, and percent methane content of the gas. Training of the neural network model was achieved using a large amount of experimentally obtained reactor performance data from the reactor mentioned above as the training set. Training was followed by validation using independent sets of performance data obtained from the same UASB reactor. Subsequently, simulations were performed using the validated neural network model to determine the impact of changes in parameters like influent chemical oxygen demand (COD) concentration and hydraulic retention time on the reactor performance. Simulation results thus obtained were carefully analyzed based on qualitative understanding of UASB process and were found to provide important insights into key variables that were responsible for influencing the working of the UASB reactor under varying input conditions.     

Steady-state and transient behavior in microbial methanification: II. Mathematical modeling and verification

It has been shown that the Upflow Anaerobic Sludge Bed (UASB) system data reported earlier(1) cannot be explained by simple Monod-type substrate consumption patterns. An autoinhibition model was also ruled out because the substrate concentration range over which hysteresis was observed was much larger than such a model would predict. However, propionic and acetic acids were found to inhibit each other's conversion machineries. Since in the UASB system the biocatalyst is flocculated, it was found that a model additionally incorporating this facet of the reactor set-up could explain the steady-state data very well. Using the parameters generated from steady-state data and data from butyric acid step change,(1) i.e., the entire set of parameters (Table I), a very good agreement between predicted and observed data was found. International Mathematical and Statistical Libraries (IMSL) and Upjohn's NONLIN library combined with various root-finding and integrating subroutines were used for parameter estimation. The model thus described was used to predict the response of the UASB system when acetic acid and propionic acid influent concentrations were stepped-up/down. The agreement between the predicted and observed data was found to be excellent in each case during the step-up schedule. During the step-down the data seemed to indicate that the UASB system, like any other chemostat, responded faster than predicted. This could be due to the fact that when the culture has to "gear up" part of the lag time is the time required for the cell to produce the requisite amount of enzymes. In the case of "gearing down" this time is not required and the system responds faster.     

HIV model parameter estimates from interruption trial data including drug efficacy and reservoir dynamics

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3-5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients.     

A simplified model of hydrodynamics in airlift loop reactors

As a function of the gas throughput the following parameters were measured in an external loop reactor with a riser diameter of 0.6 m and a gassed liquid height of 8.6 m: integral and local values of gas hold-up; liquid velocities; mixing times and axial dispersion coefficients of the liquid phase. The height of the reactor could be altered by reconstruction. Measurements were also carried out with lower heights than 8.6 m. Besides pure water, aqueous solutions of coalescing, non-coalescing and viscosity-increasing substances were used as model systems. With the results a general relationship between superficial gas velocity, gas hold-up and liquid velocity was established. This hydrodynamic model uses the relative velocity between gas and liquid phase as the fundamental parameter. The generally valid model consists of one term for the homogeneous and of two additional terms for the heterogeneous flow regime.     

Modeling of two-phase anaerobic process treating traditional Chinese medicine wastewater with the IWA Anaerobic Digestion Model No. 1

The aim of the study was to implement a mathematical model to simulate two-phase anaerobic digestion (TPAD) process which consisted of an anaerobic continuous stirred tank reactor (CSTR) and an upflow anaerobic sludge blanket (UASB) reactor in series treating traditional Chinese medicine (TCM) wastewater. A model was built on the basis of Anaerobic Digestion Model No. 1 (ADM1) while considering complete mixing model for the CSTR, and axial direction discrete model and mixed series connection model for the UASB. The mathematical model was implemented with the simulation software package MATLABTM/Simulinks. System performance, in terms of COD removal, volatile fatty acids (VFA) accumulation and pH fluctuation, was simulated and compared with the measured values. The simulation results indicated that the model built was able to well predict the COD removal rate (−4.8–5.0%) and pH variation (−2.9–1.4%) of the UASB reactor, while failed to simulate the CSTR performance. Comparing to the measured results, the simulated acetic acid concentration of the CSTR effluent was underpredicted with a deviation ratios of 13.8–23.2%, resulting in an underprediction of total VFA and COD concentrations despite good estimation of propionic acid, butyric acid and valeric acid. It is presumed that ethanol present in the raw wastewater was converted into acetic acid during the acidification process, which was not considered by the model. Additionally, due to the underprediction of acetic acid the pH of CSTR effluent was overestimated.     

Hydraulics of laboratory and full-scale upflow anaerobic sludge blanket (UASB) reactors

Laboratory-scale upflow anaerobic sludge blanket (UASB) reactors are often used as test platforms to evaluate full-scale applications. However, for a given volume specific hydraulic loading rate and geometry, the gas and liquid flows increase proportionally with the cube root of volume. In this communication, we demonstrate that a laboratory-scale reactor had plug-flow hydraulics, while a full-scale reactor had mixed flow hydraulics. The laboratory-scale reactor could be modeled using an existing biochemical model, and parameters identified, but because of computational speed with plug-flow hydraulics, mixed systems are instead recommended for parameter identification studies. Because of the scaling issues identified, operational data should not be directly projected from laboratory-scale results to the full-scale design.     

Maximum likelihood estimation of neutral model parameters for multiple samples with different degrees of dispersal limitation

In a recent paper, I presented a sampling formula for species abundances from multiple samples according to the prevailing neutral model of biodiversity, but practical implementation for parameter estimation was only possible when these samples were from local communities that were assumed to be equally dispersal limited. Here I show how the same sampling formula can also be used to estimate model parameters using maximum likelihood when the samples have different degrees of dispersal limitation. Moreover, it performs better than other, approximate, parameter estimation approaches. I also show how to calculate errors in the parameter estimates, which has so far been largely ignored in the development of and debate on neutral theory.     

Kinetics of anaerobic purification of industrial wastewater

As a part of the development of an integral mathematical model describing the up-flow anaerobic sludge blanket (UASB) reactor, the kinetics of the conversion of organic wastes has to be known. We compared the Monod model with the model proposed by Andrews et al. Together with the assumption that the substrate for the anaerobic bacteria is formed by nonionized, volatile fatty acids, the Andrews model is able to describe substrate inhibition and reactor failure due to pH changes.From four batch experiments, with different concentrations of microorganisms, it could be concluded with a reliability of over 95% that the monod model was inadequate and Andrews' model was adequate to describe the measurements. Standard statistical techniques like the X2- and the F-test were used for this purpose.From a parameter sensitivity analysis for the Andrews model it followed that the maximum specific growth rate mu(A) (max) of the bacteria and the inhibition constant K(1) are the parameters which influence the system most. Thus, these parameter were determined experimentally and most accurately. The results are: \documentclass{article}\pagestyle{empty}\begin{document}$$\mu;{A}_{\max} = 16*10;{-4}{\rm h};{-1}\pm 2\%\quad {\rm and}\quad K_l = 0.0158\,{\rm g}\,{\rm HAc/L}\pm 2.5\%$$\end{document} The other parameters were taken from literature. From calculation of the Thiele modulus for the particles it follows that transport limitation of the substrate in the flocus is not significant. The efficiency eta is 0.85 in the worst case.     

Practical identifiability of biokinetic parameters of a model describing two-step nitrification in biofilms

Parameter estimation and model calibration are key problems in the application of biofilm models in engineering practice, where a large number of model parameters need to be determined usually based on experimental data with only limited information content. In this article, identifiability of biokinetic parameters of a biofilm model describing two-step nitrification was evaluated based solely on bulk phase measurements of ammonium, nitrite, and nitrate. In addition to evaluating the impact of experimental conditions and available measurements, the influence of mass transport limitation within the biofilm and the initial parameter values on identifiability of biokinetic parameters was evaluated. Selection of parameters for identifiability analysis was based on global mean sensitivities while parameter identifiability was analyzed using local sensitivity functions. At most, four of the six most sensitive biokinetic parameters were identifiable from results of batch experiments at bulk phase dissolved oxygen concentrations of 0.8 or 5 mg O(2)/L. High linear dependences between the parameters of the subsets (KO2,AOB,muAOB) and (KO2,NOB,muNOB) resulted in reduced identifiability. Mass transport limitation within the biofilm did not influence the number of identifiable parameters but, in fact, decreased collinearity between parameters, especially for parameters that are otherwise correlated (e.g., muAOB) and KO2,AOB, or muNOB and KO2,NOB). The choice of the initial parameter values had a significant impact on the identifiability of two parameter subsets, both including the parameters muAOB and KO2,AOB. Parameter subsets that did not include the subsets muAOB and KO2,AOB or muNOB and KO2,NOB were clearly identifiable independently of the choice of the initial parameter values.     

Identification in an anaerobic batch system: global sensitivity analysis, multi-start strategy and optimization criterion selection

Several mathematical models have been developed in anaerobic digestion systems and a variety of methods have been used for parameter estimation and model validation. However, structural and parametric identifiability questions are relatively seldom addressed in the reported AD modeling studies. This paper presents a 3-step procedure for the reliable estimation of a set of kinetic and stoichiometric parameters in a simplified model of the anaerobic digestion process. This procedure includes the application of global sensitivity analysis, which allows to evaluate the interaction among the identified parameters, multi-start strategy that gives a picture of the possible local minima and the selection of optimization criteria or cost functions. This procedure is applied to the experimental data collected from a lab-scale sequencing batch reactor. Two kinetic parameters and two stoichiometric coefficients are estimated and their accuracy was also determined. The classical least-squares cost function appears to be the best choice in this case study.     

植物空间分布格局中邻体距离的概率分布模型及参数估计

最近邻体法是一类有效的植物空间分布格局分析方法,邻体距离的概率分布模型用于描述邻体距离的统计特征,属于常用的最近邻体法之一。然而,聚集分布格局中邻体距离(个体到个体)的概率分布模型表达式复杂,参数估计的计算量大。根据该模型期望和方差的特性,提出了一种简化的参数估计方法,并利用遗传算法来实现参数优化,结果表明遗传算法可以有效地估计的该模型的两个参数。同时,利用该模型拟合了加拿大南温哥华岛3个寒温带树种的空间分布数据,结果显示:该概率分布模型可以很好地拟合美国花旗松(P.menziesii)和西部铁杉(T.heterophylla)的邻体距离分布,但由于西北红柏(T.plicata)存在高度聚集的团簇分布,拟合结果不理想;美国花旗松在样地中近似随机分布,空间聚集参数对空间尺度的依赖性不强,但西北红柏和西部铁杉空间聚集参数具有尺度依赖性,随邻体距离阶数增加而变大。最后,讨论了该模型以及参数估计方法的优势和限制。     

In situ measurement of archaeal and bacterial specific growth rates in two stage high rate anaerobic treatment systems

The thymidine assay is applied and evaluated as a direct measure of archaeal and bacterial volumetric growth rate in the first and second stages of a full scale High Rate Anaerobic Treatment system (HRAT). By coupling the method to an epifluorescent microscopic technique we show how to measure microbial specific growth rates in situ. In the first stage reactor, the acidogenic (hydrolytic-fermentative) apparent bacterial specific growth rate measurements (2.2 d –1 ) agreed with that predicted by the hydraulic residence time. For the methanogenic archaeal populations in the second stage upflow anaerobic sludge blanket (UASB) reactor the measurement was the same as published values. The results also showed that in the UASB reactor the archaeal growth dynamics in the liquid phase and 'sludge' granules were the same.     

Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method

MOTIVATION: Time-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints. RESULTS: In this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing.     

A model to describe the performance of the UASB reactor

A dynamic model to describe the performance of the Upflow Anaerobic Sludge Blanket (UASB) reactor was developed. It includes dispersion, advection, and reaction terms, as well as the resistances through which the substrate passes before its biotransformation. The UASB reactor is viewed as several continuous stirred tank reactors connected in series. The good agreement between experimental and simulated results shows that the model is able to predict the performance of the UASB reactor (i.e. substrate concentration, biomass concentration, granule size, and height of the sludge bed).     

NEE观测误差分布类型对陆地生态系统机理模型参数估计的影响——以长白山温带阔叶红松林为例

基于观测数据的陆地生态系统模型参数估计有助于提高模型的模拟和预测能力,降低模拟不确定性.在已有参数估计研究中,涡度相关技术测定的净生态系统碳交换量(NEE)数据的随机误差通常被假设为服从零均值的正态分布.然而近年来已有研究表明NEE数据的随机误差更服从双指数分布.为探讨NEE观测误差分布类型的不同选择对陆地生态系统机理模型参数估计以及碳通量模拟结果造成的差异,以长白山温带阔叶红松林为研究区域,采用马尔可夫链-蒙特卡罗方法,利用2003～2005年测定的NEE数据对陆地生态系统机理模型CEVSA2的敏感参数进行估计,对比分析了两种误差分布类型(正态分布和双指数分布)的参数估计结果以及碳通量模拟的差异.结果表明,基于正态观测误差模拟的总初级生产力和生态系统呼吸的年总量分别比基于双指数观测误差的模拟结果高61～86 g C m-2 a-1和107～116 g C m-2 a-1,导致前者模拟的NEE年总量较后者低29～47 g C m-2 a-1,特别在生长旺季期间有明显低估.在参数估计研究中,不能忽略观测误差的分布类型以及相应的目标函数的选择,它们的不合理设置可能对参数估计以及模拟结果产生较大影响.