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Methodology for modeling detailed imperfect mixing effects in complex reactors
AIChE Journal
Abstract
A powerful new modeling technique is presented for exploring mixing effects in reactive flow systems. The technique combines the detailed mixing representation of computational fluid dynamics (CFD) simulations with the simplicity and computational efficiency of stirred-tank compartment models. The method can be generally applied to many reactive systems, and requires only that appropriate criteria be specified to select compartment models from a single converged CFD simulation. A 1000-fold increase in computational speed is achieved by the new compartment model/CFD technique when modeling steady-state operation of low-density polyethylene (LDPE) autoclave reactors, making broad studies of operating conditions and stability possible. Results from compartment models are shown to capture the accuracy and detail of CFD simulations over a wide range of LDPE reactor operation, and the new technique provides a combination of modeling detail and computational ease not previously available for this type of reactor. © 2005 American Institute of Chemical Engineers AIChE J, 2005
... While this empirical approach of developing compartment models is still in active use, [6][7][8] including our recent development 8 that demonstrates its capabilities in capturing the three-dimensional convective flow effect in a stirred tank reactor, it is also obvious that using the empirical coefficients to formulate exchange flow rates is not able to capture the turbulent flow in a shorter timescale compared to convective flow. Thus, the advantages of incorporating CFD predicted hydrodynamics into compartmental models (in other words, CFD-based reduced-order compartment models 9 ) have recently been demonstrated in many applications, such as multiphase reactors, 10,11 crystallization, 12 liquidliquid extraction, 13 polymerizations, [14][15][16] and bioreactors. 17,18 In the process of developing a CFD-based compartment model, there are two main approaches to incorporate the CFD-level information, and each can bring unique advantages to the compartment model. ...
... 17,18 In the process of developing a CFD-based compartment model, there are two main approaches to incorporate the CFD-level information, and each can bring unique advantages to the compartment model. The first avenue is to formulate the exchange flow rates between the neighboring compartments by aggregating the CFD cells/nodes near the compartmental interface, [9][10][11][12][13][14][15][16][17][18][19][20] which enables a more detailed representation of the flow physics (including macroscale convection and meso-scale turbulence 9 ) compared to the empirical correlation [6][7][8] that merely treats all the exchange flow rates equivalently as a constant value. Once exchange flow rates are formulated, the spatial variations of additional physics/chemistry influenced by the flow physics can be investigated, such as droplet size distribution, 10,13 gas holdup profile, 11 and chemical conversion. ...
... Once exchange flow rates are formulated, the spatial variations of additional physics/chemistry influenced by the flow physics can be investigated, such as droplet size distribution, 10,13 gas holdup profile, 11 and chemical conversion. [14][15][16]18 However, while most of the works mentioned above [10][11][12][13][14][15][16]18 have benefited from the CFD-based formulation of exchange flow rates, the system volume is still segmented manually based on the empirical knowledge of the specific flow pattern, resulting in a high cost and uncertainty of model development. 21 This limitation motivates the second approach that utilizes a simplified base-case CFD simulation to automatically compartmentalize the system volume, significantly reducing trial-and-error efforts. ...
While computational fluid dynamics (CFD)‐based compartment models have gained popularity as a cost‐effective alternative to full CFD modeling of complex mixing systems, model development involves significant trial‐and‐error efforts. This work presents a generalized zoning framework for the streamlined development of CFD‐based compartment models with detailed characterization of the reduced‐order representation of the flow physics. With a stirred tank as an illustrative case, reduced‐order model for species transport and heat transfer with turbulent flow is derived, followed by introducing the generalized zoning framework to demonstrate how a reduced‐order compartment model can be constructed based on a simplified CFD simulation. A test case of mixing two miscible thermal fluids is used to evaluate the CFD‐based compartment model. The results demonstrate that the proposed zoning framework exhibits an accurate representation of the CFD simulation of hydrodynamics and demonstrates capabilities of capturing species and heat transfer in turbulent flow systems with complex geometric configurations.
... An improvement of the geometry-based division method is to take into account explicitly the flow structure but also the chemical mechanisms if present in the reactor. Wells and Ray (2005) were the first to automate a division procedure. To do so, they implemented physical and/or chemical criteria in their division method based on reactive CFD results. ...
... With this approach, it is possible to diminish considerably the number of compartments compared to CFD, but the division is systematical and independent from the hydrodynamic, chemical or thermal phenomena. A second method consists in dividing the volume by taking into account the characteristic times of the chemical reactions (Guha et al. 2006) or the concentration of chemical species (Gresch et al. 2009;Wells and Ray 2005). With this method, the compartments sizes and shapes are not necessarily uniform. ...
... It can be noticed that only convective fluxes were considered in Nauha and Alopaeus (2013) and Wells and Ray (2005 ...
To take into account the impact of hydrodynamics on their behavior, chemical reactors are traditionally modeled as an association of smaller ideal reactors: perfectly stirred or plug flow reactors. This modeling is mainly based on the reactor hydrodynamics but sometimes also on phenomena governing the considered process such as heat or mass transfer or chemical reaction. The approaches encountered in the literature start from the most basic one in which the whole reactor is considered as an ideal reactor, up to a very fine discretization using Computational Fluid Dynamics (CFD). In between, the reactor can be described as an association of a small number of ideal reactors: this is the systemic approach. Another intermediate approach has also been recently developed: the compartmental method, where all compartments are assumed to be perfectly mixed. In the compartment method, the compartment number is significantly more important than in the systemic approach - but lower than for CFD. Furthermore, these compartments are chosen to be relevant regarding their position in space as opposed to systemic models in which, in most of cases, only the global physical behavior is taken into account. Compared to CFD, compartment models are less computationally demanding while taking into account the most important flow features. The present review describes the different types of modeling commonly used in chemical reaction engineering during the last 60 years from the systemic approach to CFD, with a focus on the attractive compartmental modelling. In particular, the methodologies encountered to determine the compartment structure are detailed, as well as the different possibilities to determine the turbulent fluxes between compartments.
... Furthermore, the exchange between the zones is modeled via volume flows, which are calculated from averaged velocities derived from the flow simulation. The use of such compartment model approaches in the context of multi-phase systems can already be found in the literature for different applications, see, e. g., [AKK99], [AKKM02], [LAA02], [PB], [VDV02], [WR05], or [KBM06]. The idea of these approaches is to take into account how the turbulent flow field in the different regions of the tank influences the population dynamical (or other) processes, but, at the same time, to avoid the enormous computing times needed for solving the full coupled system. ...
... Remark 5.2. In the literature, one can already find such kind of multi-compartment models in combination with CFD simulations for different applications, like stirred liquidliquid systems (see, e. g., [AKK99], [AKKM02], or [PB]), stirred gas-liquid systems (see, e. g., [LAA02] or [VDV02]), or imperfect mixing in reactive systems (see, e. g., [WR05]). In these papers, the compartment model approach has been combined with different solution strategies for the population balance equation, namely with the method of classes (see [AKK99], [AKKM02], [LAA02], or [VDV02]) and the method of moments (see [WR05]). ...
... In the literature, one can already find such kind of multi-compartment models in combination with CFD simulations for different applications, like stirred liquidliquid systems (see, e. g., [AKK99], [AKKM02], or [PB]), stirred gas-liquid systems (see, e. g., [LAA02] or [VDV02]), or imperfect mixing in reactive systems (see, e. g., [WR05]). In these papers, the compartment model approach has been combined with different solution strategies for the population balance equation, namely with the method of classes (see [AKK99], [AKKM02], [LAA02], or [VDV02]) and the method of moments (see [WR05]). ...
... The free-radical polymerization of ethylene within a pressurized reactor is highly spatially dependent [4]. The build-up of contiguous volumes at high temperatures affects the polymerization process which directly impacts the properties of the polymer produced. ...
... Δ represents a change in the manipulated variable, n denotes time step, e represents error, and t is time. The controllers solve for A from the Arrhenius equation using Equation 4 considering the error from the previous two-time steps. Altering the pre-exponential constant is physically realistic as the five controllers throughout the reactor are in regions with varying reactivity. ...
... The free-radical polymerization of ethylene within a pressurized reactor is highly spatially dependent [4]. The build-up of contiguous volumes at high temperatures affects the polymerization process which directly impacts the properties of the polymer produced. ...
... Δ represents a change in the manipulated variable, n denotes time step, e represents error, and t is time. The controllers solve for A from the Arrhenius equation using Equation 4 considering the error from the previous two-time steps. Altering the pre-exponential constant is physically realistic as the five controllers throughout the reactor are in regions with varying reactivity. ...
... In literature compartment-models have been used for homogeneous reactors (Alexopoulos et al., 2002;Wells and Ray, 2005;Guha et al., 2006;Gresch et al., 2009;Le Moullec et al., 2010), bubble columns (Bauer and Eigenberger, 1999), airlift reactors (Rigopoulos and Jones, 2003), gas-liquid stirred tank reactors (Vrábel et al., 1999;Laakkonen et al., 2006;Gimbun et al., 2016), crystallizers (Kramer et al., 1996;Kulikov et al., 2005;Irizarry, 2008bIrizarry, , 2008aIrizarry, , 2012Metzger and Kind, 2014) and granulation processes (Bouffard et al., 2012;Yu et al., 2017). In cooling crystallization, the formation of crystals, the super-saturation and the temperature profile strongly influence each other. ...
... In further investigations, different compartment grid resolutions have to be analyzed in more detail, for example by comparing tracer simulations. Other methods for automatically choosing the grid resolution are given by , and Wells and Ray (2005). At the top of the domain, water loaded with 0:025 kg=kgof transfer component (acetone) flows into the extraction area. ...
In multiphase devices, fluid dynamics have a high impact on concentration profiles and mass transfer between the phases and therefore influence efficiency. Standard models often assume ideally mixed conditions or plug flow. The application of such models for multiphase devices with complex flow patterns causes inaccuracies, if the flow deviates from ideally mixed or plug flow conditions. Therefore, for a precise model based design and operation parameter determination of devices with complex flow patterns, the local fluid dynamics should be considered. CFD simulations for multiphase systems including mass transfer, population balance equations for coalescence and breakage as well as reactions are still time consuming. Thus, we developed a compartment-model based on prior calculated CFD flow-data. In the CFD simulations, the time consuming population balance equations for coalescence and breakage, mass transfer and reactions are neglected. These phenomena are considered in the compartment-model. Thereby we reduce the overall computing time.
This paper presents the CFD based compartment-model applied on a loop-reactor. First, a three-phase CFD model of the developed multiphase loop-reactor is introduced. Following, the paper presents the compartment-model and the application of a time-driven constant-number Monte-Carlo approach to solve population balances. Finally, the compartment-model is applied to the liquid-liquid extraction part of the loop-reactor calculating the drop size distribution and mass transfer based on previously calculated CFD data.
... The definition of compartments and the exchange flows has always been the main challenge of compartment modelling. Up to today, manual configuration of the network of compartments has been the most cited strategy in the scientific literature ( Wells and Ray 2005;Le Moullec et al. 2010;Bashiri et al. 2014;Bashiri et al., 2016;Nauha et al. 2018 ). Vrábel et al. used a CM to simulate the mixing behavior in a 30 m 3 aerated reactor with multiple impellers ( Vrábel et al. 1999 ). ...
... The exchange flows could be extracted from a CFD model ( Kougoulos et al., 2005 ). Wells et al. followed a similar approach by introducing a compartmentalization method based on successive subdivision of the simulation domain into spatial regions, where they show small variations in the target variables ( Wells and Ray 2005 ). The biggest advantage of this approach was its ease of implementation, but there was no guarantee that the cells belonging to a zone were continuous. ...
Computational fluid dynamics (CFD) is a powerful tool for quantitative prediction of fluid dependent properties in a finite volume. However, the complexity of solving the momentum balances and the continuity equations at each element of the discretized geometry can easily lead to an expensive computational task. Compartment modelling is a potential alternative to speed up the calculation, which is however reached at the expense of the level of accuracy. The most important factor in optimizing a compartment model (CM) concerning the accuracy and the computational time is the quality of the chosen compartments to represent the critical gradients. This work presents a new automated compartmentalization method to characterize an improved network of compartments derived from initial detailed CFD results, with a focus on cylindrical-shaped systems. This method was evaluated with a case study of a 700 L stirred tank bioreactor by estimating the mixing performance and demonstrating its high efficiency.
... Automation also eases the increase of zone number from a few dozens up to some hundreds of zones. However, to date, only two efforts have been published to address the task of automating the zoning process: The region splitting method presented by Wells and Ray [WeR05] and the region growing method of Bezzo and Macchietto [BeM04]. The two methods will be examined more closely, but first, the general concept of a zoning method is introduced. ...
... In region splitting the whole domain initially represents a single zone which is sequentially split until it satisfies the homogeneity conditions, as described in Algorithm 1. Wells and Ray [WeR05] presented an automatic zoning algorithm based on a region splitting method which they applied to an autoclave reactor producing low-density polyethylene. Their zoning algorithm sequentially divides and subdivides the computational domain along CFD cell boundaries until predetermined number of zones is reached. ...
... This approach is less computationally demanding, as the flow between compartments are given as an input to the model, and the mass and momentum balances are not included (avoiding the fine CFD discretization). The traditional approach to compartment modelling is to define the compartment network manually [6][7][8][9][10][11]. This step introduces a large amount of uncertainty to the model as the volumes and exchange flowrates are arbitrarily chosen to fit experimental data or based on a priori knowledge of the mixing behaviour of the system. ...
This article aims to develop a method to automatically generate CFD-based compartment models. This effort to simplify mixing models aims at capturing the interactions between material transport and chemical/biochemical conversions in large-scale reactors. The proposed method converts the CFD results into a system of mass balance equations for each defined component. The compartmentalization method is applied to two bioreactor geometries and was able to replicate tracer mixing profiles observed in CFD simulations. The generated compartment models were successfully coupled with, a simple Monod-type biokinetic model describing microbial growth, substrate consumption and product formation. The coupled model was used to simulate a four-hour fermentation in a 190 L reactor and a 10 m3 reactor. Resolving the substrate gradients had a clear impact on the biokinetics, increasing with the scale of the reactor. Moreover, the coupled model could simulate the fermentation faster than real-time. Having a real-time-solvable model is essential for implementations in digital twins and other real-time applications using the models as predictive tools.
... In phenomenological models [392][393][394][395][396][397][398], the flow pattern and/or the polymerization temperature are calculated per distinct zone and exchange or recycle flows are considered to reflect the occurrence of imperfect mixing or temperature gradients at the macro-scale. In many cases, these zones can be linked to the residence time distribution, which describes the fraction of fluid elements staying in the reactor as a function of reaction time. ...
Polymers are composed of macrospecies that are characterized by a broad range of molecular variations such as chain length, functionality, comonomer composition, branching density, and crosslinking amount that can be controlled through (i) a plethora of macromolecular chemistries and (ii) many reactor configurations and operations. To fully grasp and exploit these control handles, it is strongly recommended (i) to develop modeling tools that are synergetic with experimental methods and (ii) to identify which in silico tool is suited most in which context. In the present chapter, we give an overview of the most important in silico multiscale tools for macromolecular chemistry and engineering. This is done by addressing both deterministic and stochastic modeling approaches, allowing application at both lab and industrial scale. We first explain how computational chemistry (e.g., ab initio calculations) can contribute to the understanding and tuning of chemical reactivities and chain interactions, thus molecular scale phenomena. This illustrated through a Case study 2.1 on controlled radical polymerization. We then introduce the concept of microscale modeling to map the competition of chemistry and diffusional limitations, as polymerization processes are very prone to viscosity increases. Specific emphasis is on the benchmarking of the popular method of moments and the recently more employed matrix-based kinetic Monte Carlo simulations (Case study 2.2) as well as machine learning tools. Mesoscale modeling tools are subsequently discussed to enable the description of multiphase/particulate polymerizations such as emulsion polymerization or the synthesis of high impact polymeric materials. A Case study 2.3 is devoted to surface initiated polymerization. We further elaborate on macro-scale modeling tools that allow to account for scale-up effects, due to nonhomogeneity in temperature and mixing intensities. Here we specifically deal with the recent advances in computational fluid dynamics (CFD) simulations, as illustrated through a Case study 2.4. Finally, we link the already introduced multiscale polymer reaction engineering approaches with the field of materials science.
... Nevertheless, little has been done to account for the effect of non-ideal mixing while simulating kinetics. Implementation of the kinetics model into a CFD-based compartmental model (CM) overcomes the challenges of the computational stiffness by solving differential equations of the kinetic model into the CFD model at a lower computational time and with improved accuracy [15][16][17][18]. ...
Understanding mixing behavior and its impact on conversion processes is essential for the operational stability and conversion efficiency of anaerobic digestion (AD). Mathematical modelling is a powerful tool to achieve this. Direct linkage of Computational Fluid Dynamics (CFD) and the kinetic model is, however, computationally expensive, given the stiffness of the kinetic model. Therefore, this paper proposes a compartmental model (CM) approach, which is derived from a converged CFD solution to understand the performance of AD under non-ideal mixing conditions and with spatial variation of substrates, biomass, pH, and specific biogas and methane production. To quantify the effect of non-uniformity on the reactor performance, the CM implements the Anaerobic Digestion Model 1 (ADM1) in each compartment. It is demonstrated that the performance and spatial variation of the biochemical process in a CM are significantly different from a continuously stirred tank reactor (CSTR) assumption. Hence, the assumption of complete mixed conditions needs attention concerning the AD performance prediction and biochemical process non-uniformities.
... Compartment models have been applied for homogeneous reactors (Alexopoulos et al., 8 2002;Wells and Ray, 2005;Guha et al., 2006;Gresch et al., 2009;Le Moullec et al., 2010), 9 ...
The simulation of stirred liquid–liquid extraction columns with CFD still requires significant computing resources. Therefore, a CFD-based compartment model was developed for a simulation of a representative amount of drops while keeping the computing effort low. The model is based on the velocity profile of the continuous phase generated by a single-phase CFD simulation. The drop movement, mass transfer, accumulation of the dispersed phase under stators, coalescence, and breakage are modeled according to this flow profile. The simulation of the fluid dynamics is in good agreement with published experiments of a DN80 Kuehni extraction column.
... The convective fluxes are calculated solving mass balance equations and the turbulent fluxes are calculated using the results of turbulence fields simulations. Wells and Ray (2005) used a compartmental approach to study mixing effects in complex polymerisation reactors. They first ran a simplified CFD simulation with the reaction of the autoclave reactor; they wanted a model to obtain temperature and concentration fields. ...
Compartmental modelling is a hybrid way to model complex systems in Chemical Engineering. This modelling approach offers numerous advantages because it aggregates information from both local and system scale models. Compartmental models allow multi-scale modelling with low computational time compared to a full coupled model (e.g. reactive numerical simulations). Thanks to these main characteristics, compartmental models are able to model complex full-size industrial systems.
For the last decades, various approaches of compartmental models were developed for different applications. In this article, a critical review and analyses are carried out to classify these different approaches. A unified definition is proposed, and important guidelines are pointed out to assist with constructing a Compartmental Model.
Finally, some perspectives for the future of Compartmental Modelling are identified and discussed: compartmental modelling for larger and more complex systems, the inclusion of new phenomena modelling and automation of compartmental models with the improvement of numerical methods.
... The aim of the compartmentalization approach is to describe the imperfect mixing by defining the large scale fluid system as a network of finite-number interconnected ideallymixed sub-volumes that contain no or negligible gradients (Wells andRay, 2006, Nauha et al., 2018). The compartmental zones can be decided based on several criteria such as flow pattern, gradients of temperature and concentration, solid distribution or local energy dissipation (Kougoulos et al., 2006). ...
... CMs have been applied to characterize the culture conditions in bioreactors ( 14,46,72,95,116,147 ; W. 154 ). Furthermore, entire bioprocesses have been simulated. ...
... Compartment models have been used earlier to investigate the influence of non-ideally mixed reactors on ldPE polymerization (Wells and Ray, 2005a, 2005b, 2005cVilla et al., 1998). In compartment models, two or more continuous stirred tank reactors in series are considered together in such a way that the main flow is from one reactor to another downstream, while eventually a small backflow from upstream reactors is assumed to account for 'backmixing'. ...
Modeling of the molecular weight distribution (MWD) of low-density Polyethylene (ldPE) has been carried out for a tubular reactor under realistic non-isothermal conditions and for a series of CSTR׳s. The model allows for the existence of multiradicals and the occurrence of gelation. The deterministic model is based on a Galerkin finite element approach (FEM) and employs the pseudo distribution concept to address the number of radical sites per chain as the second dimension next to chain length. The Galerkin method is shown to allow a straightforward and compact formulation of the series of CSTR׳s using a repetitive matrix structure with connective elements. The ‘topological scission’ model is utilized as the closest approximation of random scission in deterministic modeling accounting for the highly branched character of the system As conditions of ldPE polymerization lead to broad MWD and are close to gelation, allowing for gel turns out to be crucial. It was observed that a broad MWD in a single CSTR becomes narrower as the number of CSTR׳s in series increases and is narrowest in the batch reactor.
... Wells and Ray [WeR05] presented a region splitting method focusing on minimizing variations in an autoclave reactor core kinetic rates, temperature and composition. Their zoning algorithm sequentially divides the computational domain along CFD cell boundaries until predetermined number of zones is reached. ...
... Although a general term, we define our mesoscale as an element approximately 0. 25 cm 3 in size in which we perform computational fluid dynamic (CFD) calculations. Many publications use CFD modeling to describe micromixing in single-phase polymerization reactors 4,5 . Other authors use CFD to model multiphase reactors, such as gas-liquidsolid 6 or gas-solid fluidized beds 7 . ...
... Recently, a third approach relying upon the combination of CFD and CM modeling is emerging (Bezzo et al., 2003;Rigopoulos and Jones, 2003;Wells and Ray, 2005;Guha et al., 2006;Laakkonen et al., 2006;LeMoullec et al., 2010). It consists of solving the turbulent liquid flow by CFD and, then, of developing a compartment model based on the CFD results. ...
... Eq. (13) is a first-order upwind discretization of the convection term. First-order discretization of the convective flux has also been chosen by other researchers dealing with reactive flow (Brucato et al., 2000), especially when compartmental modelling is applied (Bezzo et al., 2003;Rigopoulos and Jones, 2003;Wells and Ray, 2005). This is probably due to the higher computational expense and complexity of more accurate discretizations. ...
A method is proposed to simulate reactive flow, fully taking into account the effect of the reactions on the flow. Operator splitting is used to separate the computation of convection and reaction. A fast solver for mildly stiff ordinary differential equations and parallelization of the reaction term evaluation have been implemented to reduce the CPU time. The proposed method is applied to the steady-state, two-phase gas–solid simulation of a Fluid Catalytic Cracking riser reactor. A relatively simple kinetic model with four lumped components is used to demonstrate the feasibility of the method. The results show that the method is able to handle reactive flow with significant feedback of the reactions on the flow.
Low‐Density Polyethylene (LDPE) reactors have the potential for rupture because of thermal runaway from auto‐accelerating chemistry. Pockets of unmixed, highly reactive, LDPE constituents, called hot spots, are often generated by conditions within the reactor and are the main source of thermal runaway. Because of this, there is a need to define thresholds of hot spot conditions that produce runaway. Computational Fluid Dynamics is used to study an isolated LDPE sphere with varying initial temperature, initial catalyst concentration, and volume to determine which combinations promote thermal runaway. It is found that increasing both initial temperature and initial catalyst concentration increased thermal runaway likelihood, while, counter‐intuitively, hot spot volume has no effect. An LDPE runaway map is provided to quantify the combinations that result in safe reactor operation. This allows manufacturers to make more informed control actions and to determine safe reactor conditions based on local mixture composition and temperature alone.
CFD‐based compartment (CPT) models offer a promising modeling method and trade‐off between computational effort and required accuracy. The models combine the relevant fluid dynamics from the computational expensive CFD and the incorporation of complex reaction mechanisms usually used in basic reactor models. However, one criticism is their reliance on specific operating points, rendering them invalid when boundary conditions change. This study explores using a CFD‐based CPT model for static mixing elements across multiple operating points by making use of the creeping flow. The mean age theory facilitates a comprehensive comparison between CFD and CPT models. Results indicate that within this flow region, the CPT model can be extrapolated to other operating points via linear scaling.
Shortstopping reactions via injection of chemical inhibitors is a promising technique of emergency response to prevent thermal runaway, with unique advantages of cost effectiveness and process sustainability over current evacuation practices. However, computational modeling of the inhibition process for ensuring successful designs remains challenging. In this paper, a compartment model is developed to investigate the design of the inhibition system with detailed characterization in both complex kinetic mechanism and nonideal mixing effect. The reactor volume is divided into a network-of-zones (NoZ), with each zone modeled as a well-mixed reactor. The free-radical solution polymerization of methyl methacrylate (MMA) in a stirred batch reactor is used as a demonstrative example. The flow parameters and network structure of compartment models are validated with the CFD simulation. The developed compartment models are employed to investigate interactions of poor mixing and exothermic chemistry that lead to thermal runaway and key design factors including injection location, quantity, kinetic requirement, and timing on the effectiveness of quenching thermal runaway.
What is digitalization, and why do we need it? What does digitalization mean for research and development in polymer reaction engineering (PRE)? In this chapter, we address these questions, starting from a global perspective, briefly analyzing the current situation. We then illustrate our views on how the virtual representation of a polymerization process, i.e., a digital twin, would enable us to widen the spectrum of research and development in PRE. The main tasks of the digital twin are, in our opinion, to approach two yet unsolved problems: linking reaction conditions to final material properties and producing materials in an optimal way. Our strategy to tackle these issues is to combine physical and data science models. We analyze how the predictive ability of deterministic approaches, such as kinetic, thermodynamic and fluid mechanics models is improved by parameters and mechanistic understanding provided by quantum chemistry and molecular dynamics. While we constantly aim for a deeper physicochemical understanding to improve these physical models, we recognize the power of statistics and machine learning, as they enable us to approach highly complex problems, thanks to their large flexibility. When analyzing the current limitations of each technique, we believe that concrete progress can only be achieved if we systematically centralize our knowledge. Therefore, we conclude our perspective on digitalization in PRE by advocating for initiatives that foster an open source sharing of published experimental data, parameters, models, and algorithms.
AD mixing is usually assumed to be uniform, and its kinetic process and performance predicted using simple models like continuously stirred tank reactor (CSTR), mostly ignoring the digester hydrodynamics. However, achieving uniform AD mixing is challenging because of the viscous nature of the sludge. Computational fluid dynamics (CFD) models are applied to study the non-ideal mixing of AD, but most often ignore the biokinetics. The limitations of both approaches are addressed in this work by integrating the kinetics and hydrodynamics of the CFD model and using a CFD based compartmental model (CM) approach. The latter was applied in this work as it is a promising non-ideal kinetics modelling method that is relatively fast compared to a CFD approach. In this dissertation, more attention was given to CFD modelling since a detailed understanding of the mixing process is a prerequisite for the accurate non-ideal kinetic modelling of the digester based on CFD-based CM. The work started from simple models and built step by step to more advanced models. The AD mixing hydrodynamics using axial flow impeller was studied, treating the sludge as a Newtonian fluid for TSS less than 4% and non-Newtonian using a Herschel-Bulkley rheology model for sludge TSS greater than 4% to understand the digester hydrodynamics first and then derive a compartmental model for non-ideal kinetics model. The non-uniformity of AD mixing based on velocity distribution was classified into high, medium, low, and stagnant velocity zones to compartmentalize the digester. The volumes of the compartments are calculated using cumulative volume distribution of velocity. The effects of the non-ideal mixing model on specific biogas production, biomass, pH, substrate distribution, and effectiveness digester volume are assessed and compared with CSTR digester implementing ADM1 into both CM and CSTR digester. CM showed that mixing affects the performance of AD, and biochemical process spatial variation differs from the CSTR kinetics model. The effect of diffusion transport on scalar variables like soluble substrates and biomass are modelled integrating part of ADM1 into the CFD model using a User-Defined Scalar (UDS). Scalar transport leads to understanding mixing uniformity under advection-diffusion and sole advection transport. Moreover, mixing non-uniformity description in terms of concentration of scalar variables distribution was proposed rather than velocity distribution. AD mixing uniformity description based on velocity and scalar variables' concentration distribution does not lead to the same conclusion. Hence it leads to further investigations implementing mixing time analysis and tracer residence time distribution (RTD). Mixing time modelling under advection-diffusion transport by injecting a tracer into the stagnant velocity zone is investigated for a detailed understanding of mixing behavior in addition to scalar variables distribution. The tracer mixing time distribution at different locations within low and stagnant velocity zones showed that uniform tracer concentration distribution is achieved irrespective of velocity magnitude. The validity of scalar concentration distribution and mixing time models uniformity against non-uniform velocity distribution was investigated, implementing the kinetic model into a full-scale CSTR AD and comparing with measured data. Specific biogas and methane production comparison of the measured data and CSTR AD model shows that the measured data is lower than the modelled results. This indicates the existence of other factors that affect AD mixing, which cannot be expressed using velocity distribution, concentration distribution, and mixing time. Short circuit flow and local recirculation effects are the factors that cannot be expressed using the variables discussed. The impact of short circuit flow and local recirculation effects on AD mixing are investigated, implementing a virtual tracer test under advection-diffusion transport in CFD modelling and compared with that of CSTR AD. The mixing non-uniformity analysis combining the velocity streamline, velocity vectors, and residence time distribution (RTD) of the tracer identify that a stagnant zone inside the digester is due to local recirculation flows. It was also understood that the stagnant volume is not only due to low-velocity zones, as described in the literature. Instead, it is mainly due to recirculation flow in all digester velocity zones. The combined study of the virtual tracer test, scalar variables, and velocity streamline/vector lead to the conclusion that AD mixing non-uniformity cannot be described based on one variable. The finding of this dissertation concludes that AD mixing is non-ideal, and non-uniformity of AD mixing can be described better based on the combination of two or more variables for an accurate representation of the CFD model. Kinetics modelling of AD integrating with CFD model is yet to be done and validated. Therefore, the non-ideal kinetic model using a CM, derived from combined velocity vector, scalar variables, and RTD of the tracer gives a detailed spatial and temporal variation of the AD kinetic process, which are highly important in digester optimum mixer design, mixing optimization and operation of the digester. It is recommended to include this detail in the system analysis and in a practical setting rather than ignoring it.
For detailed simulation and evaluation of stirred extraction columns a CFD based compartment‐model was developed. Instead of simulating all effects in a computational expensive PBE‐CFD‐model, the velocity field calculation of the continuous phase is decoupled from the calculation of the dispersed phase (one‐way coupling). In CFD only the continuous phase is simulated and the resulting velocity profile is used in the compartment‐model to simulate the drop movement, coalescence, breakage and mass transfer for a representative number of drops (Monte‐Carlo Method). This decoupling has a major impact on the calculated fluid‐dynamics. Thus, the velocity profile of the CFD results is modified in the model to account for phase interaction. The compartment‐model is applied for the simulation of a Kühni extraction column with the system toluene/water/acetone. The simulation results, namely holdup, drop size and concentration profiles over the column height, are in good agreement with experiments for different loads and different stirrer speeds.
This work presents an in silico tool that supports crystallization process development and optimization studies by means of mechanistic modeling, uncertainty identification, comprehensive sensitivity analysis and a quantified process risk assessment. Kinetic model parameters and operation design parameters are considered as a source of uncertainty and variation. Monte Carlo simulations are performed to propagate input uncertainty/variation to model output in terms of process yield, mean crystal diameter and size distribution. To quantify the individual effects and importance of these parameters, global sensitivity analysis e.g. Morris Screening and variance-based decomposition, is performed. The process risk is defined as failure to reach target product specifications and its consequences for the given design space is quantified. This promising study shows, that global uncertainty and sensitivity analysis coupled with the quantification of process risk assessment is a powerful tool and should be of interest to those participating in effective and efficient crystallization process development.
A compartment modeling approach based on computational fluid dynamics (CFD) simulations is applied to a simplified static mixer geometry. Compartments are derived from velocity fields obtained from cold CFD simulations. This methodology is based on the definition of periodic flow zones (PFZ) derived from the recurrent flow profile within the static mixer. In general, PFZ can be characterized by two different compartments: flow zones with hydrodynamic behavior of a tubular reactor and dead zones exhibiting a more continuous stirred tank reactor‐like characteristic. In CFD studies the influence of changing fluid properties, for example viscosity, on flow profile due to polymerization progress is considered. In the deterministic compartment model, the continuous flow profile within the static mixer is transformed to basic reactor models interconnected via an exchange stream. To reduce model complexity and the number of model parameters, constant volumes of compartments are assumed. Changes in hydrodynamics are considered by a variable exchange flow rate as a function of Re manipulating residence time in compartments. Simulation studies show the influence of decreasing exchange flow rates with polymerization progress, as Re decreases, resulting in a greater increase of viscosity in dead zones. The reactor performance is qualitatively represented by the simulation results. A compartment modeling approach for continuous polymerization reactors based on computational fluid dynamics simulations is presented. The compartments are derived from velocity fields, differentiating flow zones from dead zones with increased residence time. The continuous flow profile is transformed to compartments—basic reactor models—which are connected via variable exchange streams to account for changes in hydrodynamics with reaction progress.
A segregation-backmixing model is developed to simulate the dynamic operation of multi-feed high pressure LDPE autoclaves, calculate the specific initiator consumption (grams of initiator per kilogram of LDPE) and assess the risk of ethylene decomposition under different nonideal mixing and operating scenarios. To describe the non-ideal macro and micromixing phenomena in a LDPE autoclave, a user-specified multi-zone model representation of the actual reactor is established. One of the key features of the present model is that the continuously fed initiator into a reaction zone can exhibit two distinct states, namely, a “segregated” or a “molecular” one. Simulation results are presented showing the effects of macromixing and micromixing model parameters on the spatial temperature distribution, specific initiator consumption with respect to the initiator feed concentration to a two-compartment reaction zone. Finally, the operational conditions and process faults that can lead to ethylene decomposition in a reaction zone are investigated.
Thermal stability is a crucial issue for fluidized bed ethylene polymerization reactors, especially when the particle aggregation probability increases due to the high reaction temperature or operation under the condensed mode. To determine the mean particle size, a population balance model (PBM) considering particle growth and particle aggregation was implemented in the present study. Then an integrated model including the two-phase model (TPM), the PBM and an evaporation model was proposed to describe polymerization of ethylene in liquid-containing fluidized bed reactors. The results demonstrate that the particle growth rate and catalyst particle size dominate the particle size of the final product. Thermal stability of fluidized bed reactors is mainly affected by the catalyst activation energy, the superficial gas velocity, and the condensed liquid flow rate.
In this work, the decomposition reaction of ethylene is investigated in a high‐pressure view cell. Thus, for the first time, it is possible to precisely determine the velocity and structure of the flame front under high pressure. On one hand, the experiments should provide a better understanding of the decomposition process in a time and spatially resolved manner but also about the chemistry‐turbulence interaction. On the other hand, the experiments serve as a basis and validation for the development of a numerical simulation model. The flame front propagation after a thermal decomposition of ethylene is investigated under high pressure. For this purpose, the experiments are performed in a view‐cell autoclave and recorded with a high‐speed camera. As a result, a correlation for the flame‐front speed can be defined as a function of pressure and temperature.
A computational fluid dynamics (CFD) approach, coupled with anionic polymerization kinetics, was used to investigate the solution polymerization in a 12 m³ industrial scale cis-polybutadiene reactor. The kinetic model with double catalytic active sites was integrated with CFD by a user-defined function. The coupled model was successfully validated by the plant data and then used to investigate the key operating variables. Also, predictions of CFD model were compared with those of continuous stirred tank reactor (CSTR) model. Although the reaction mixture is well mixed in the middle and at the top of the reactor, there exists a poor mixing feeding zone at the bottom, which leads to serious deviations from the ideal CSTR. The polymerization process with nonideal mixing is very sensitive to the inlet temperature and the feeding rate. Enhancing the mixing performance in the feeding zone could be an effective way to improve the product quality.
A computational fluid dynamics (CFD) approach coupled with polymerization kinetics is implemented to investigate styrene polymerization using azobisisobutyronitrile (AIBN) as initiator and toluene as solvent in a lab-scale continuous stirred tank reactor (CSTR). The integration of kinetic model and CFD model taking molecular weight distribution into consideration is accomplished by a user-defined function (UDF) code using the method of moments. The results predicted by CFD compare with literature data satisfactorily. The effects of operating variables such as species diffusion coefficient, impeller speed, residence time and reaction temperature are analyzed. As the impeller speed increases, the degree of mixing homogeneity is improved, which results in decreasing conversion and molecular weight distribution. The proposed method can be used to predict polymerization behaviors in non-ideal mixing industrial reactors.
Molecular weight distribution (MWD) is essential for describing the microstructural quality of a polymer. However, most of the studies on MWD are limited to ideal reactors. Computational fluid dynamics (CFD) methods is a useful tool to deal with the nonideal reactors. Few studies on CFD have been extended to the simulation and optimization of polymer MWD due to the computational difficulties. In this study, a new strategy is proposed to simulate the spatial MWD for a type of nonideal reactors using the method of moments with interfacing to the CFD software. Subsequently, given a target MWD curve, process optimization is proposed to achieve the optimal operating conditions. The tubular and autoclave reactors of the low-density polyethylene process are demonstrated for the simulations and optimizations. The influences of the decision variables on the feasibility and objective function are also discussed.
Process Description Multiscale Modeling Opportunities Modeling a Mesoscale Packed Bed Using CFD Predicting Solubility from Molecular-Scale Fundamentals Closing Remarks References
Fermentation is the conversion of renewable feedstock into useful products, with the help of the help of microorganisms. This chapter discusses the separation of the real bioreactor volume in two or more virtual compartments, in which the fluid flow follows an idealized pattern, with recirculation between the compartments, but in which the conditions for the cells are different. It describes some new elements of bioreactor modeling that will be needed to scale up more bioprocesses to commercial scale, and to bring new fermentation&;#x02010;based products to the market. More advanced is the application of computational fluid dynamics (CFD) models, in which local details can be estimated using the governing equations for mass and momentum conservation, with assumptions for description of the turbulence, and source and sink terms to account for the substrate uptake and product formation kinetics. The compartment modeling approach and structured segregated modeling approaches are also discussed.
The degree of mixing in polymerization reactions can be influenced by various factors that can also affect the reactor performance. For this reason, a detailed micromixing model was implemented to study the effects of micromixing on the dynamic behavior of continuous free-radical solution polymerization tank reactors. The reactor model was used to perform the bifurcation analysis of the reacting system, paying special attention to the effect of micromixing parameters on the reactor behavior. The bifurcation study showed that multiple steady-states and periodic oscillations can be observed under partially segregated micromixing conditions. Moreover, the micromixing model was able to describe the dynamic responses presented by perfectly mixed and completely segregated reactors. These results indicate that this class of reactors can exhibit more complex dynamic behavior than shown until now.
Molecular weight distribution (MWD) is essential for describing the microstructural quality of a polymer. In the past decade, the simulation and optimization of the MWD of a polymerization process have received considerable attention. However, most studies are limited to ideal reactors, such as CSTRs. However, in large-scale industrial reactors, imperfect mixing often leads to a non-uniform distribution. The commercial software Fluent is used in this study to simulate free radical polymerization by the method of moments and computational fluid dynamics (CFD). An interface is designed in-house to extend the simulation to MWD calculation. Given a specific MWD curve as the target, process optimization is performed by combining CFD and MWD calculations in the in-house developed interface between C language and Fluent. A non-ideal tubular reactor is demonstrated for the low-density polyethylene process.
The strength of multi-scale modeling to support the fundamental understanding and design of radical polymerization processes is illustrated, considering both controlled and free radical polymerization (CRP/FRP) in non-dispersed (bulk/solution) and dispersed (suspension/emulsion) media. At the molecular scale, the importance of joint experimental and theoretical studies is highlighted. At the micro-scale, the concept of apparent rate coefficients is elaborated to account for the possible influence of diffusional limitations on the local reaction rates. At the meso-scale, the key characteristics to fundamentally describe the evolution of the particle size distribution are covered and the possible interaction with the micro- and macro-scale is discussed. At the macro-scale, the main mathematical tools to assess the relevance of mixing and temperature gradients are provided. Several examples on CRP and FRP processes are included to showcase the modeling capabilities for each scale, focusing both on laboratory and industrial reactors.
Understand quantitative model step-growth polymerization plans and how to predict properties of the product polymer with the essential information in Step-Growth Polymerization Process Modeling and Product Design. If you want to learn how to simulate step-growth polymerization processes using commercial software and seek an in-depth, quantitative understanding of how to develop, use, and deploy these simulations, consult this must-have guide. The book focuses on quantitative relationships between key process input variables (KPIVs) and key process output variables (KPOVs), and the integrated modeling of an entire polymer manufacturing train.
Blasensäulenreaktoren sind zwar mechanisch einfache Apparate, die in ihnen vorherrschenden Gas-Flüssig-Interaktionen sind aber bedeutend komplexer. Die Auslegung anhand des axialen Dispersionsmodells hat entscheidende Nachteile in der Beschreibung der komplexen Wechselwirkungen zwischen Gas- und Flüssigphase. Obwohl die numerische Strömungsmechanik in den letzten Jahren, auch aufgrund steigender Rechnerkapazitäten und -leistungen, sehr vielversprechende Fortschritte gemacht hat, ist die Berechnung des Betriebsverhaltens industrieller Blasensäulenreaktoren nicht verifizierbar. Als Alternative bieten sich eine Unterteilung des Reaktors in Teilbilanzräume an. Diese als Kompartment-Modellierung bekannte Beschreibungsmethode wird im Rahmen des Beitrags erläutert und diskutiert.
Bubble column reactors are mechanical simple apparatuses, but the interactions between the liquid and gas phases have proven to be more complex. The description with an axial dispersion model has significantly disadvantages describing those physical phenomena. Although numerical fluid dynamics promising progress, not only backed by the increase in computational power and capacities, these calculations are not yet verifiable for industry sized reactors. An alternative approach is to divide the reactor in smaller material balance envelopes. This approach, known as compartment modeling, is explained and discussed in this article.
A population balance model for the prediction of molecular weight distribution (MWD) in a continuous stirred tank reactor (CSTR) has been developed accounting for multiradicals and gel formation in the framework of Galerkin-FEM. In the absence of recombination, gel does not form, but accounting for multiradicals leads to a better prediction of the long MWD tail. Results of the multiradical model with topological scission are well in line with Monte Carlo (MC) simulations. For the case of recombination without scission the multiradical model leads to perfect agreement with MC simulations as regards prediction of the gel fraction and chain length distribution. The classical monoradical model fails to describe the gel regime. We account for gel fragmentation in systems with gelation and scission. Results for this case are in agreement with MC simulations. A nongel assuming variant allows properly detecting the gelpoint and the associated distribution. The scission model adopted, linear or topological scission, turns out to be of extreme importance for the gel regime prediction.
The autoclave reactor offers flexibility in producing specialty grades of ethylene/vinyl acetate copolymer at temperature range of 150-230 °C and pressure range of 1400-2000 kg/cm2. At such conditions, copolymerization is accompanied by decomposition of reactants which increases the risk of thermal runaway. The runaway reaction is initiated by local hot spots in the reactor which are generated by process/equipment disturbances or imperfect mixing in the reactor. It is hard to predict decomposition due to the extremely fast dynamics of the event. A decomposition detection method was developed based on the overall energy balance around the reactor. During normal steady state operations, the heat balance error should be within reasonable limits. If abnormal conditions generate excess heat in the reactor, the heat balance error will exceed the limit indicating the possibility of an impending decomposition. Principal component analysis (PCA) was used for model identification and to get the unknown parameters in the model. Iterative PCA technique was used to confirm the selection of the model. Long term plant operation data over the period of six months was used for training and testing of the model. Data validation rules were applied and false alarms associated with operating conditions fluctuations were minimized by applying appropriate equations for conversion at various operating conditions. The model was validated with an actual plant steady state decomposition case where the model could predict decomposition with few seconds of lead time. This article is protected by copyright. All rights reserved
The present study describes the development of a nonhomogeneous two-compartment model for the prediction of particle size distribution in a semibatch emulsion ter-polymerization reactor. The multicompartment model accounts for spatial variations of particle size distribution (PSD) in the reactor due to nonideal mixing conditions. A comprehensive emulsion polymerization model is applied to each compartment, which allows the calculation of the various species concentrations in the aqueous and particle phases in each compartment. Moreover, a particle population balance equation is solved for each compartment to determine the individual PSDs as well as the overall PSD in the reactor. The effects of the two-compartment nonhomogeneous model parameters, that is, the volume ratio of the two compartments, the compartment exchange flow rates, and the partitioning of the monomer and initiator feed streams into the two compartments, on the overall polymerization rate and PSD are analyzed in detail. It is shown that depending on the selected values of the two-compartment model parameters, the overall PSD in the reactor can significantly vary (i.e., from a narrow and/or broad unimodal distribution to a bi- and/or multimodal PSD). Small compartment exchange flow rates, uneven monomer and initiator feed partitioning, or unequal compartment volumes can result in very different PSDs in the two compartments. Moreover, it is shown that for a range of parameter values in the two-compartment model (i.e., reflecting the degree of reactor nonhomogeneity), the calculated overall PSD in the industrial-scale reactor can be unimodal but significantly broader than the respective PSD calculated by the homogeneous one-compartment model.
A new compartmental Monte Carlo (CMC) algorithm is introduced for the stochastic simulation of population balance models in spatially heterogeneous systems. The heterogeneities are modeled using a network of compartments. The algorithm is based on a new stochastic procedure called particle bundle flow (PBF) to model the stochastic transfer of particles between compartments in a given time interval (a time-driven algorithm). Different from other time-driven methods, the accuracy of the PBF is independent of the particle concentration. The validity of the PBF method is demonstrated by construction and confirmed with numerical experiments. A new strategy for time step control is developed to set bounds on the calculation of the time steps during the simulation. The CMC algorithm, based on the combination of the PBF algorithm with the τ point ensemble Monte Carlo algorithm, is a general-purpose methodology that can be applied to any network of compartments. The computational speed and the low computational load of this algorithm allow the solution of problems that may be intractable otherwise. A new hybrid strategy for the solution of problems with stochastic fluctuations and disparate time scales is also developed in this work. The CMC is applied to study the formation of nanoparticles in a large reactor utilizing a two-compartment model. The Monte Carlo ability to track single events is utilized to study the impact of turbulence and the stability factor on the generation of large particles.
Imperfect initiator mixing greatly affects the stability and efficiency of low density polyethylene (LDPE) autoclave reactors. A combined simulation technique utilizing compartment models and computational fluid dynamics extends previous work in the literature by providing a physically detailed picture of imperfect mixing. Analysis indicates that the effective volume for chain propagation in the autoclave reactor can expand and contract in a continuous fashion as operating conditions change. As mixing becomes poor, the effective reactive volume decreases, causing a reduction in initiator efficiency, but an expansion in the stable operation region. Examples demonstrate that accurate prediction of the effective reaction volume is crucial for predicting LDPE autoclave reactor behavior. A new mixing model that represents the feed plume by a series of interconnected tanks with geometrically increasing volumes provides a favorable tradeoff between accuracy and model complexity. © 2005 American Institute of Chemical Engineers AIChE J, 2005
Flow and reaction in a typical commercial scale autoclave LDPE reactor were modeled by a three-dimensional computational fluid dynamic (CFD) k-∈ model in order to shed light on the macrosegregation effects that can occur in these reactors. It is shown that the CFD model predicts significant differences from CSTR behavior. Results are discussed in terms of the effects of macro- and microscale inhomogeneities of concentration and temperature on free radical polymerization kinetics. The observed nonidealities in terms of minima in the initiator consumption curves and multiple steady states are explained on the basis of competing turbulent transport and chemical kinetics. Microsegregation effects are shown to be negligible in comparison to macrosegregation effects. Given the fact that the CFD model is based on reactive scalar and energy balances without adjusted parameters in the three-dimensional flow field of the entire reactor, it is tentatively concluded that commercial-scale LDPE vessel reactors can have significant macrosegregation effects beyond a certain steady-state adiabatic operating temperature that is specific to the initiator being used.
A critical issue in the modeling of aerobic bioreactors is the close interaction between fluid flow and the biological reactions. In particular, shear rate has a large effect on the broth viscosity which, in turn, affects the rate of mass transfer of oxygen from the gas to the liquid phase. We demonstrate how a generic hybrid multizonal/computational fluid dynamics (CFD) modeling approach can be applied to take account of these interactions. The approach to multizonal modeling presented characterizes the flow rates between adjacent zones, and also the fluid mechanical quantities, such as the shear stress, that have important effects on the process behavior within each zone, by means of steady-state CFD calculations. An unstructured model for xanthan gum production in a batch aerobic bioreactor is used for this purpose. The hybrid modeling approach is also applied to structured models involving distributions of cell mass within each zone.
The paper reviews the problem of making numerical predictions of turbulent flow. It advocates that computational economy, range of applicability and physical realism are best served at present by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour. The width of applicability of the model is demonstrated by reference to numerical computations of nine substantially different kinds of turbulent flow.
Two completely different processes are used for the manufacture of LDPE (low-density polyethylene): the tubular reactor process and the stirred autoclave process. The author points out the main differences between these two processes and goes into details of the autoclave process. The largest autoclaves with a volume of more than 1. 0 m**3 operate with pressures of about 1500 to 2500 bars and at temperatures between 130 and 280 degree C. Stirred autoclaves permit precisely adjustable reaction conditions and therefore guarantee highest safety in operation and reproducibility of polymer properties. The autoclave process offers considerable advantages for manufacturing copolymers.
In spite of the widespread use of the stirred vessel gas/liquid reactor in the chemical industry, there is still no satisfactory unified description of the internal two phase mixing processes. A comprehensive engineering treatment will need to combine the physical flow of gas and liquid with the interphase transfer, which in turn must be integrated with both the macro and micro mixing. Recent progress on these problems is discussed, continuing on the approach developed in an Industrial Research Fellowship Report. The networks of zones concept appears to be a promising basis for the development of a unified theory. (A)
Most polymerization reactions proceed at a faster rate under high pressure. Higher molecular weights are obtained at higher pressures. High pressure polymerizations of a wide variety of vinyl type monomers and copolymerizations of two or more monomers have been investigated by many researchers around the world.1–8 Such studies have been conducted with free radicals derived from oxygen and organic peroxides, photoinitiation,9,10 and high energy radiation.11 High pressure polymerizations have also been conducted with anionic12 and cationic13 initiators (catalysts) and with transition metal catalysts.14
A computer model was developed for tubular high-pressure polyethylene reactors. Plug flow and absence of axial mixing were assumed. Emphasis was placed on realistic modeling of the reaction kinetics and the variation of physical properties along the reaction coordinate. A good simulation of axial temperature profiles, conversion, molecular weights, molecular weight distribution, and transport properties along the reaction coordinate is believed to have been achieved. The model can be extended readily to cases where radial diffusion is significant.
The way in which reagents are mixed can have a large influence on the product distribution of a chemical reaction. This has been analysed earlier when micromixing is the limiting mixing step. Additional segregation at a larger scale has only been treated in detail when the local turbulent dispersion of a feed stream was relevant. Here additional segregation due to the finite disintegration rate of large concentration eddies is represented by a feasible structure to describe the environment within which micromixing and chemical reaction take place. The resulting model contains one time constant each for micro- and mesomixing. Their estimation is discussed and applied to predicting the yields of fast complex reactions in plug-flow static mixers and in a semibatch stirred tank reactor under conditions where neither macromixing nor turbulent dispersion were limiting. The comparison with measured yields is good for micromixing and fairly satisfactory for inertial-convective mesomixing. Further research on this step is needed.
This paper identifies a number of key issues regarding the development of general modelling languages for combined lumped and distributed parameter processes, and proposes one such language. The latter has been implemented in the gPROMS process modelling system and permits the mathematical modelling of arbitrarily complex unit operations that are distributed over rectangular domains in terms of mixed systems of integral, partial differential, and algebraic equations (IPDAEs). Following language translation, validation and analysis, the method of lines is employed automatically to convert the IPDAEs to sets of ordinary differential-algebraic equations (DAEs). The latter are then solved simultaneously with the DAEs that model the behaviour of the lumped parameter units in the process. Three examples are presented to illustrate the capability of the proposed modelling system to deal with a wide variety of complex processes described in terms of IPDAEs.
The basic ideas for modelling micromixing, given in Part II, are applied to a pair of consecutive, competitive reactions conducted in semibatch as well as in continuous stirred tank reactors. The objections to earlier work, given in Part I, no longer apply, The principles of calculating the product distribution X for each reactor type are outlined and numerical results are given, using the parameters for the diazo coupling of 1-naphthol with diazotised sulphanilic acid. These showed the dependence of X on mode of reactor operation (SBR and CSTR), volume ratio of reagent solutions (VA/VB), Schmidt number (Sc) and mixing modulus (M = k2cB0δv /DA). Under typical experimental conditions, the first reaction was instantaneous, whilst the second was fast (see Appendix), permitting a transformation of composition variables and an enormous saving of computer time.Measured product distributions for the diazo couplings were available covering two tank sizes, three impeller types, three volume ratios, several initial concentrations of reagents, semibatch and continuous operating modes and several feed points. These points were grouped together as (a) suction side of impeller, (b) just below liquid surface, and (c) midway between impeller and wall. (The only major independent variable not covered here is fluid viscosity). In order to make a prediction with the new model, only the rate of energy dissipation (ϵ) in the reaction zone must still be known. This was expressed as a multiple (φ) of the average rate(ϵ = ϵ) and the values consistent with the product distributions measured for the three feed points were (a) 8, (b) 0.23, and (c) 1. These are in good agreement with flow visualisations as well as local ϵ-measurements using hot film and laser doppler anemometry. These and other results suggest that the new model represents a significant advance on previous methods
The objectives are to identify the key physical processes contributing to mixing on the molecular scale, using information from Fluid Mechanics, and to construct a corresponding mathematical model. The concentration spectrum indicates that molecular diffusion and hence micromixing starts towards the fine scale end of the viscous-convective subrange and becomes dominant in the viscous-diffusive subrange. Such small fluid elements are subject to laminar deformations at rates proportional to (ϵ/v)1/2. Their thickness is related to shear rate and time using a result from the statistical theory of turbulent diffusion, valid in the viscous subrange at short times. One result is that the diffusion field rapidly becomes one-dimensional. Numerical calculation confirms that fluid elements, initially of Kolmogoroffsize, first deform and that diffusion becomes significant only at still smaller scales. The assignment of an initial length scale is therefore not critical.The role of vorticity for small eddies, where energy dissipation and laminar deformations occur, is discussed. Vortices provide the mechanism to form laminar structures by engulfing the fluid in their immediate environment. The frequency of vortex formation is determined. Diffusion and reaction occur within deforming laminated structures temporarily trapped inside stretching vortices. At the end of vortex activity, as the fluid has returned temporarily to isotropy, a new burst of vorticity creates a further generation of vortices out of old vortex material and its surroundings. This description applies to liquid mixing, for which Sc » 1 i.e. diffusion is much slower than momentum transfer. Mixing, brought about by these periodic processes, ends when the concentration is uniform at the molecular scale.
The series treats the mixing on the molecular scale (micromixing) of two miscible streams to bring about reaction between their constituents. The case where mixing and reaction have similar time constants is particularly interesting, although the framework is also valid for slow and instantaneous reactions. The case of fast reactions is important because no generally valid modelling is yet available, although examples of such reactions are now known. Two competitive, consecutive reactions are analysed in detail, where the yield of the intermediate product falls rapidly as inhomogeneity and concentration gradients on the molecular scale increase.Part I shows that no existing formulation of micromixing is sufficiently general. The model of lamellar structures (or double slab model) excludes mass exchange between a flow element and its environment and thus, applied to a continuous reactor, permits only a description of segregated flow i.e. other flow situations are incorrectly described, as is also illustrated with examples. A diffusion-reaction model, originating from this laboratory, artificially confined one of the reagents to a single slab, where all diffusion and reaction steps were assumed to occur. This is too restrictive and can lead to errors, which are again illustrated with examples. Both approaches concentrate on the final, diffusive stage of mixing. They overlook the preceding convective steps and are useless for estimating the mixing time. Again examples are given.
The networks-of-zones model has been used to analyse the mixing behaviour in three dimensions when a cold slug of quenchant material is injected into a batch of reactants. In this way, it is possible to make predictions of the conditions required for achieving a safe quench when a reaction is close to a runaway condition. Some illustrations are presented typical of styrene polymerization using 0(104) zones in a stirred autoclave. The dynamic responses of sets of thermocouples arranged within the reacting fluid form a convenient basis for validation of the model. The complexities of compositional and temperature changes, together with the consequent reaction rates, are conveniently predicted from integration of sets of ordinary differential equations. The model fluid flow parameters can be easily deduced from simple tracer visualization tests.
The original version of the networks-of-zones (N-o-Z) model developed for the description of gas–liquid flow in stirred-vessel reactors (R. Mann, Gas–liquid stirred vessel mixers: towards a unified theory based on network of zones, Transactions of the Institution of Chemical Engineers 64 (1986) 23–34) has been extended and enhanced to cover distributed bubble sizes, gas–liquid mass transfer, bioreaction kinetics and multiple-impeller operation. In addition, a modified version of the N-o-Z model for bubble columns has been simply derived from the impeller version, assuming the existence of a two-loop axisymmetrical circulation pattern induced by the non-uniform distribution of gas holdup in bubble columns. The liquid circulation velocity has been expressed as a function of gas flow rate and the density difference between the gas and liquid phases, based on Zehner's circulation model (P. Zehner, G. Schuh, A concept for the description of gas phase mixing in bubble columns, German Chemical Engineering 5 (1985) 282–289). These two variants of the N-o-Z model have been used for modelling three different industrial fermenters: 3 and 31m3 triple-impeller stirred reactors, and a 236m3 bubble column reactor. The performance of these three reactors, typical of the fine chemicals, bioprocessing and pharmaceutical process industries was evaluated and compared in terms of geometry/size, gas flows, power inputs, pressure, liquid mixing, oxygen mass transfer, reaction speed and spatial variability of behaviour. This provides potentially valuable insights into the relative factors influencing the selection of an appropriate reactor type.
The fluid phase reaction A+B→R to a desired product, when accompanied by a parallel decomposition to a by-product A→S, form a pair of reactions ideal for evaluating mixing-with-reaction tests. The reactions are typical of diazotisation in dyestuff manufacture, so that fundamental mixing studies can be linked to practical manufacturing. Earlier studies on these problems used a 2-D analysis which is approximate for some practical cases. This approach has now been extended to a full 3-D network-of-zones for a stirred vessel for single-point dip-pipe addition at any location. This is a simplified computationally tractable approach to fluid mixing, which is superior to more complex CFD solutions, because it can easily handle multiple complex reactions. The flow and mixing in the 3-D network incorporates axial and radial convection with swirling tangential flow, turbulence and flow around baffles. Computations are then tractable for long duration semi-batch addition modes of operation. Macro-mixing (in 3-D), the associated partially segregated fields of reagents A and B and the spatial-temporal evolution of the local instantaneous yields and selectivities are illustrated using solid-body AVS graphics for the Drain/ICI reactions.
This paper concerns the mathematical modelling of a catalytic process carried out in a non-isothermal fluidized-bed reactor. A three-phase multi-compartment model of the fluidized bed is used for elucidating the hydrodynamics of the bed as well as for the simulation of a non-isothermal catalytic process. A basic version of the reactor model is proposed and two simplified models are developed. One assumes the stagnation of the gas in the emulsion phase within each compartment distinguished by the model; the other, for the case of back flow of the gas, assumes homogeneity of the concentration field in the emulsion phase. Both assumptions which have been introduced are discussed quantitatively and in detail. Some numerical computations have been performed for the purpose of comparing the degree of conversion and temperature distribution obtained according to different models. The Kunii—Levenspiel model and two multi-compartment models were considered. An analysis of the multiplicity of steady states has also been carried out. Hysteresis loops were obtained in the fluidization ratio—emulsion temperature system of coordinates. Over a certain range of feed temperature two separate areas of multiple steady states were shown to exist.
A mathematical model is developed for the calculation of polymer quality in low density polyethylene vessel reactors, taking into account mixing limitations at the initiator feed point. Model predictions show that imperfect mixing in the reactor can produce considerable variations in polymer molecular weight distribution. The effect of the most important process conditions, input feed temperature, solvent concentration, monomer flow rate and initiator type, on the final polymer quality is analyzed. The advantages of the design solution which divides the reactor in more compartments in series are also discussed.
Recently, a novel algorithmin situ adaptive tabulationhas been proposed to effectively incorporate detailed chemistry in computational fluid dynamics (CFD) simulations for turbulent reacting flows. In this work, detailed tests performed on a pairwise-mixing stirred reactor (PMSR) model are presented implementing methane thermochlorination chemistry to validate the in situ adaptive tabulation (ISAT) algorithm. The detailed kinetic scheme involves 3 elements (H, C, Cl) and 38 chemical species undergoing a total of 152 elementary reactions. The various performance issues (error control, accuracy, storage requirements, speed-up) involved in the implementation of detailed chemistry in particle-based methods (full PDF methods) are discussed. Using an error tolerance of εtol = 2 × 10-4, sufficiently accurate results with minimal storage requirements and significantly less computational time than would be required with direct integration are obtained. Based on numerous test simulations, an error tolerance in the range of 10-3−10-4 is found to be satisfactory for carrying out full PDF simulations of methane thermochlorination reactors. The results presented here demonstrate that the implementation of ISAT makes possible the hitherto formidable task of implementing detailed chemistry in CFD simulations of methane thermochlorination reactors.
Flow and reaction in a typical commercial scale autoclave LDPE reactor were modeled by a three-dimensional computational fluid dynamic (CFD) k−ε model in order to shed light on the macrosegregation effects that can occur in these reactors. It is shown that the CFD model predicts significant differences from CSTR behavior. Results are discussed in terms of the effects of macro- and microscale inhomogeneities of concentration and temperature on free radical polymerization kinetics. The observed nonidealities in terms of minima in the initiator consumption curves and multiple steady states are explained on the basis of competing turbulent transport and chemical kinetics. Microsegregation effects are shown to be negligible in comparison to macrosegregation effects. Given the fact that the CFD model is based on reactive scalar and energy balances without adjusted parameters in the three-dimensional flow field of the entire reactor, it is tentatively concluded that commercial-scale LDPE vessel reactors can have significant macrosegregation effects beyond a certain steady-state adiabatic operating temperature that is specific to the initiator being used.
With the implementation of efficient algorithms for the accurate calculation of reaction source terms, computational fluid dynamics (CFD) is now a powerful tool for the simulation and design of chemical reactors with complex kinetic schemes. The example studied in this work is the methane chlorination reaction for which the detailed chemistry scheme has 152 reactions and 38 species. The adiabatic, jet-stirred chlorination reactor used for the CFD simulations is an insulated right cylinder with a coaxial premixed feed stream at one end. In order for this reactor to remain lit, recirculation of hot products is crucial, and hence, reactor stability is sensitive to both macroscale and microscale mixing. By neglecting density variations, a Lagrangian composition probability density function (PDF) code with a novel chemistry tabulation algorithm (in-situ adaptive tabulation or ISAT) for handling complex reactions is used to simulate the species concentrations and temperature field inside of the reactor. In addition, a reduced mechanism with 21 reactions and 15 species is tested for accuracy against the detailed chemistry scheme, a simplified CSTR model is used to illustrate the shortcomings of zero-dimensional models, and a pair-wise mixing stirred reactor (PMSR) model is used to show the stabilizing effect of micromixing on reactor stability. The CFD simulations are generally in good agreement with results from pilot-scale reactors for the outlet temperature and major species.
Imperfect initiator mixing greatly affects the stability and efficiency of low density polyethylene (LDPE) autoclave reactors. A combined simulation technique utilizing compartment models and computational fluid dynamics extends previous work in the literature by providing a physically detailed picture of imperfect mixing. Analysis indicates that the effective volume for chain propagation in the autoclave reactor can expand and contract in a continuous fashion as operating conditions change. As mixing becomes poor, the effective reactive volume decreases, causing a reduction in initiator efficiency, but an expansion in the stable operation region. Examples demonstrate that accurate prediction of the effective reaction volume is crucial for predicting LDPE autoclave reactor behavior. A new mixing model that represents the feed plume by a series of interconnected tanks with geometrically increasing volumes provides a favorable tradeoff between accuracy and model complexity. © 2005 American Institute of Chemical Engineers AIChE J, 2005
Computational fluid dynamics methods are used to provide three-dimensional simulations of a low-density polyethylene (LDPE) autoclave reactor under normal operating conditions. For the conditions used, the reactor is not very well mixed; thus, the common model approximation of a perfectly stirred reactor is not warranted. The simulations verify the sensitive nature of the polymerization reactors and indicate a need for optimizing operating parameters.
By the use of an imperfectly mixed model developed for LDPE vessel reactors, we show that a linear controller cannot perform satisfactorily in the entire range of operating conditions of industrial interest. Based on the concept of reaction rate control, a novel controller is developed which provides satisfactory closed-loop dynamics independent of steady-state conditions. A nonlinear controller is shown to be more effective in avoiding reactor light-off.
To study runaway behavior in autoclave low-density polyethylene (LDPE) reactors, a kinetic model for a perfectly stirred tank reactor is presented. The kinetic model not only includes the standard initiation, propagation, and termination reactions for polymerization, but it also has free radical reactions that describe the decomposition of ethylene ultimately leading to a runaway. Dynamic simulation of the model indicates runaway behavior for the following conditions: excess initiator in feed; feed impurity; feed temperature disturbance; controller failure; and poorly tuned controller. Operating strategies such as mixed initiator feeds and grade transitions are also explored from a dynamic view. Stability analysis indicates safe operating limits for certain variables at typical conditions. The model provides useful insights for preventing runaway reactions in LDPE autoclaves.
A modelling strategy for effective estimation of the particle size distribution (PSD) in suspension polymerization is presented. The strategy consists of coupling a population balance equation (PBE) and a compartment-mixing (CM) model to account for the non-homogeneous mixing in the tank reactor. The values for the rate of energy dissipation of each compartment are estimated from Computational Fluid Dynamics (CFD) calculations and experimental reports on systems with the same agitator and geometric characteristics. Model predictions using the CM model are compared with predictions that assume homogeneous mixing and experimental data on PSD from styrene and divinylbenzene pilot-plant suspension polymerization reactors of 1 and 5 L with Rushton and PBT impellers.
On présente une stratégie de modélisation pour l'estimation de la distribution de tailles des particules (PSD) lors de la polymérisation en suspension. La stratégie consiste à coupler une équation de bilan de populations (PBE) à un modèle de mélange par compartiment (CM) pour tenir compte du mélange non homogène dans le réacteur. Les valeurs de taux de dissipation d'énergie de chaque compartiment sont estimées à partir de simulations d'écoulement par ordinateur (CFD) et de données expérimentales obtenues sur des systèmes ayant le měme agitateur et les měmes caractéristiques géométriques. Les prédictions du modèle utilisant le modèle CM sont comparées aux prédictions qui supposent un mélange homogène et à des données expérimentales sur la PSD venant de réacteurs de polymérisation en suspension de styrène et de divinylbenzène d'usine pilote, de 1 et 5 L munis de turbines Rushton et de turbines à pales inclinées.
A new analysis tool is presented that uses the governing kinetic scheme to predict properties of low‐density polyethylene (LDPE) such as the detailed shape of the molecular weight distribution (MWD). A model that captures mixing details of autoclave reactor operation is used to provide a new criterion for the onset of MWD shouldering. Kinetic effects are shown to govern the existence of MWD shoulders in LDPE reactors, even when operation is far from perfectly‐mixed. MWD shoulders occur when the mean reaction environment has a relatively high radical concentration and has a high polymer content, and is at a low temperature. Such conditions maximize long chain formation by polymer transfer and combination‐termination, while limiting chain scission. For imperfectly‐mixed reactors, the blending of polymer‐distributions produced in different spatial locations has a small effect on the composite MWD. However, for adiabatic LDPE autoclaves, imperfect mixing broadens the stable range of mean reactor conditions, and thereby increases the possibility for MWD shouldering.
Polymer MWD produced in an LDPE autoclave reactor by various kinetic mechanisms.
magnified image Polymer MWD produced in an LDPE autoclave reactor by various kinetic mechanisms.
The dynamic behavior of processing systems exhibits both continuous and significant discrete aspects. Process simulation is therefore a combined discrete/continuous simulation problem. In addition, there is a critical need for a declarative process modeling environment to encompass the entire range of processing system operation, from purely continuous to batch. These issues are addressed by this article.
A new formal mathematical description of the combined discrete/continuous simulation problem is introduced to enhance the understanding of the fundamental discrete changes required to model processing systems. The modeling task is decomposed into two distinct activities: modeling fundamental physical behavior, and modeling the external actions imposed on this physical system. Both require significant discrete components. Important contributions include a powerful representation for discontinuities in physical behavior, and the first detailed consideration of how complex sequences of control actions may be modeled in a general manner.
A compartmental model is used to study imperfect mixing and its effects on polymer properties. Examples of imperfect feed mixing caused by a rapidly decomposing initiator are shown for styrene polymerization, high-pressure ethylene polymerization, and vinyl acetate/methyl methacrylate solution copolymerization. Continuation analysis indicates mixing can change reactor steady states and stability. A composite approach is proposed to construct full molecular weight distribution (MWD) under imperfect mixing. In linear polymerization imperfect mixing broadens MWD; however, in nonlinear polymerization mixing can cause either broader or narrower MWD. By changing the dominant chaintermination mechanism to chain transfer, the influence of imperfect mixing on the MWD can be reduced. Depending on reactivity ratio and monomer composition, mixing also affects copolymer composition and chain sequence length.
By the use of a perfectly mixed model and an imperfectly mixed one for lowdensity polyethylene vessel reactors, we show that increases in the initiator consumption with polymerization temperature are due to mixing limitations at the initiator feed. With all its parameters independently estimated, the imperfectly mixed model provides an excellent agreement with experimental data for several initiators, feed flow rates and polymerization pressures. In the temperature region of industrial interest for each type of initiator, the open-loop reactor dynamics drastically change from open-loop unstable, at low temperatures, to open-loop stable at high polymerization temperatures.
Free radical copolymerization in high-pressure autoclave reactors is studied by developing a mathematical model. Kinetic mechanisms to describe the polymerization rate, molecular weight averages, branching frequencies, as well as copolymer composition are presented. Two phase kinetics due to polymer-monomer solubilities in the reaction mixture are taken into account. Gel formation from cross-linking reactions is also analyzed. A mixing model is developed to represent the stirring effect inside the reactor. The mathematical model is implemented as a computer program to simulate commercial autoclave reactors. PID control equations are used to maintain operation at the unstable steady state. A sensitivity study is performed on the mixing model parameters and on some of the kinetic parameters and the model is compared to rate data from commercial reactors.
Earlier work considered the effect of feed conditions and controller configuration on the runaway behavior of LDPE autoclave reactors assuming a perfectly mixed reactor. This study provides additional insight on the dynamics of such reacton by using an imperfectly mixed reactor model and bifurcation analysis to show the changes in the stability region when there is imperfect macroscale mixing. The presence of imperfect mixing substantially increases the range of stable operation of the reactor and makes the process much easier to control than for a perfectly mixed reactor. The results of model analysis and simulations are used to identify some of the conditions that lead to unstable reactor behavior and to suggest ways to avoid reactor runaway or reactor extinction during grade transitions and other process operation disturbances.
A comprehensive mathematical model is developed to simulate the dynamic behavior of multizone, multifeed high-pressure ethylene polymerization autoclaves. To describe the complex flow patterns occurring in low-density polyethylene (LDPE) autoclaves, a user-specified multisegment, multirecycle model representation of the actual multizone reactor is established. A general reaction mechanism is employed to represent the kinetics of ethylene polymerization. Dynamic mass, molar species, and energy balances are derived to predict the polymerization rate, monomer conversion, molecular weight developments (e.g., Mn, Mw, long- and short-chain branching), and temperature profile with respect to time and spatial position in the reactor. Detailed results on the start-up and grade transition of a four-zone autoclave reactor are presented and the effects of the macromixing parameters (e.g., number of segments per reaction zone and the total and side external recycle ratios) on the dynamic behavior of the reactor are investigated. It is shown that the model macromixing parameters can significantly affect the initiator consumption rate in a reaction zone. The present model is capable of predicting accurately the dynamic behavior of LDPE autoclaves and, thus, can be employed in the design, optimization, and control of these reactors. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 2327–2348, 1999
We develop the dynamic renormalization group (RNG) method for hydrodynamic turbulence. This procedure, which uses dynamic scaling and invariance together with iterated perturbation methods, allows us to evaluate transport coefficients and transport equations for the large-scale (slow) modes. The RNG theory, which does not include any experimentally adjustable parameters, gives the following numerical values for important constants of turbulent flows: Kolmogorov constant for the inertial-range spectrumC
K=1.617; turbulent Prandtl number for high-Reynolds-number heat transferP
t
=0.7179; Batchelor constantBa=1.161; and skewness factorS
3=0.4878. A differentialK-
[`(e)]\bar \varepsilon
model is derived, which, in the high-Reynolds-number regions of the flow, gives the algebraic relationv=0.0837 K2/
[`(e)]\bar \varepsilon
, decay of isotropic turbulence asK=O(t
–1.3307), and the von Karman constant[`(e)]\bar \varepsilon
, and[`(e)]\bar \varepsilon
is finite. This latter model is particularly useful near walls.
The relationship between Lagrangian micromixing models, which are widely employed in chemical reaction engineering, and Eulerian computational fluid dynamic (CFD) models based on the Reynolds-averaged species conservation equation is explored. A general modeling methodology which combines the strengths of both approaches is developed in the form of a multi-environment CFD micromixing model. The formulation is shown to be equivalent to a presumed multi-scalar probability density function (PDF) approach. The four-environment generalized mixing model (GMM) model originally proposed by Villermaux and Falk (Villermaux and Falk, Chem. Eng. Sci. 49 (5127) (1994)) is used to illustrate the methodology by applying it to model a series-parallel reaction in a tubular reactor.
The quantitative description of particle size distribution development in suspension polymerization reactors is very complex. The exact mechanisms of breakage and coalescence/aggregation of the polymerizing drops are generally not very well understood, and are closely related and controlled by the spectrum of turbulent energy dissipation rate in the reactor. In the present investigation, a two-compartment population balance model was developed for taking into account the large spatial variations of the local turbulent kinetic energy, in order to predict the evolution of droplet sizes in a high holdup (i.e., 47–50 vol%) suspension polymerization system as a function of the most important process conditions, such as type of suspending agent, monomer/water-phase ratio, polymerization temperature, quality of agitation, and evolution of the dispersed-phase density, interfacial tension and viscoelasticity during the polymerization. Phenomenological expressions of the literature were modified for drops in the viscous dissipation range and were applied for describing the breakage and coalescence rates of the polymerizing dispersed phase as a function of the basic hydrodynamics and evolving physical properties of the system. Computational fluid dynamics simulations were used for estimating the volume ratio of the impeller and circulation regions, the ratio of turbulent dissipation rates and the exchange flow rate of the two compartments at different agitation rates and continuous-phase viscosities. The theoretical model can predict reasonably well the experimentally observed inhomogeneities of the drop size distribution as well as the evolution of particle size distribution in VCM suspension polymerization, especially considering the various assumptions in formulating the drop breakage and coalescence rates and in the two-compartment approximation of the inhomogeneities of the turbulent flow field in the suspension polymerization reactor.
Computational fluid dynamics (CFD) and process simulation are widely used in the process industry. The two technologies are largely complementary, each being able to capture and analyse some of the important process characteristics. Their combined application can, therefore, lead to significant industrial benefits. This is especially true for systems, such as chemical reactors, in which steady-state performance, dynamics and control strategy depend on mixing and fluid flow behaviour. This paper presents a new approach for the integration of the capabilities of CFD technology and process simulation via a general interface that allows the automatic exchange of critical variables between the two packages, leading to a simultaneous solution of the overall problem. The approach applies to both steady-state and dynamic problems. The feasibility of the approach and its first practical implementation are demonstrated by integrating a widely used CFD package (Fluent 4.5, by Fluent Inc.) within a general-purpose advanced process simulator (gPROMS 1.7, by Process Systems Enterprise Ltd. (1999)). One case study involving a batch reactor is used to illustrate the ability of the combined tool to provide information on the detailed interactions between fluid mechanics, heat transfer, reaction and control strategy, and to provide insights on important design and operational decisions.
Until recent years knowledge of chemical processing was descriptive and qualitative.
In 1810 modern chemical theory was born and process description became quantitative.
Then about 1900 the quantitative engineering approach was developed, first for physical changes, called the Unit Operations, and somewhat later for chemical operations. This we call the American approach.
In 1957 European chemical engineers brought together the design of chemical and their related physical operations under the name of Chemical Reaction Engineering, or CRE. This approach and name received practically universal acceptance.
Today the methods of CRE are widely used in the processing of biochemical and all sorts of other systems,
This talk wanders through this development.
This book presents the current state of the art in computational models for turbulent reacting flows, and analyzes carefully the strengths and weaknesses of the various techniques described. The focus is on formulation of practical models as opposed to numerical issues arising from their solution. A theoretical framework based on the one-point, one-time joint probability density function (PDF) is developed. It is shown that all commonly employed models for turbulent reacting flows can be formulated in terms of the joint PDF of the chemical species and enthalpy. Models based on direct closures for the chemical source term as well as transported PDF methods are covered in detail. An introduction to the theory of turbulent and turbulent scalar transport is provided for completeness. The book is aimed at chemical, mechanical, and aerospace engineers in academia and industry, as well as developers of computational fluid dynamics codes for reacting flows.
Typescript. Thesis (Ph. D.)--University of Wisconsin--Madison, 1996. Vita. Includes bibliographical references.
Escherichia coli fed-batch cultivations at 22 m3 scale were compared to corresponding laboratory scale processes and cultivations using a scale-down reactor furnished with a high-glucose concentration zone to mimic the conditions in a feed zone of the large bioreactor. Formate accumulated in the large reactor, indicating the existence of oxygen limitation zones. It is suggested that the reduced biomass yield at large scale partly is due to repeated production/re-assimilation of acetate from overflow metabolism and mixed acid fermentation products due to local moving zones with oxygen limitation. The conditions that generated mixed-acid fermentation in the scale-down reactor also induced a number of stress responses, monitored by analysis of mRNA of selected stress induced genes. The stress responses were relaxed when the cells returned to the substrate limited and oxygen sufficient compartment of the reactor. Corresponding analysis in the large reactor showed that the concentration of mRNA of four stress induced genes was lowest at the sampling port most distant from the feed zone. It is assumed that repeated induction/relaxation of stress responses in a large bioreactor may contribute to altered physiological properties of the cells grown in large-scale bioreactor. Flow cytometric analysis revealed reduced damage with respect to cytoplasmic membrane potential and integrity in cells grown in the dynamic environments of the large scale reactor and the scale-down reactor.
This reports presents new codes for the numerical solutiuon of highly nonlinear systems. They realize the most recent variants of affine invariant Newton Techniques due to Deuflhard. The standard method is implemented in the code NLEQ1, whereas the code NLEQ2 contains a rank reduction device additionally. The code NLEQ1S is the sparse version of NLEQ1, i.e. the arising linear systems are solved with sparse matrix techniques. Within the new implementations a common design of the software in view of user interface and internal modularization is realized. Numerical experiments for some rather challenging examples illustrate robustness and efficiency of algorithm and software. Contents 0 Introduction 2 1 Global Affine Invariant Newton Techniques 4 1.1 Outline of algorithm : : : : : : : : : : : : : : : : : : : : : 4 1.1.1 Newton methods : : : : : : : : : : : : : : : : : : : 4 1.1.2 Affine invariance : : : : : : : : : : : : : : : : : : : 6 1.1.3 Natural monotonicity test : : : : : : : : : ...
An integrated process simulation and CFD environment using the CAPE– OPEN interface specifications
- Felix M P Osawe
- M Syamlal
- Cleetus I Kj Lapshin
- Zitney
- Se
Osawe M, Felix P, Syamlal M, Lapshin I, Cleetus KJ, Zitney SE. An integrated process simulation and CFD environment using the CAPE– OPEN interface specifications. Proc of AIChE Annual Meeting, Indi-anapolis, IN; 2002.