- The University of Jordan
Faculty of Engineering & Technology
Department of Chemical Engineering
11942-Amman
Jordan
- TU Kaiserslautern, Process Engineering, Graduate Studentadd
- Population Balance Modeling (Engineering), Computer-Aided Chemical Process Engineering, Algorithms, Process Optimization, Applied Mathematics, Computational Fluid Dynamics (CFD) modelling and simulation, and 6 moreComputational Modelling, Chemical Engineering, Bioengineering, Computational Fluid Dynamics, Automatic Control, and Liquid Liquid Extraction(Computational Modelling, Chemical Engineering, Bioengineering, Computational Fluid Dynamics, Automatic Control, and Liquid Liquid Extraction)edit
- - Computer-aided process engineering/ University of Kaiserslautern/ Institute of Process Engineering/ Germany with di... more- Computer-aided process engineering/ University of Kaiserslautern/ Institute of Process Engineering/ Germany with distinction grade (Auszeischnung).
- In 2008, was honored with the selection as a testimonial in the Postgraduate & Doctoral Education by the International School for Graduate Studies at the University of Kaiserslautern/ Germany
- PATENT: System and method for simulating and modelling the distribution of discrete systems, United States Patent Application: 0100106467(- Computer-aided process engineering/ University of Kaiserslautern/ Institute of Process Engineering/ Germany with distinction grade (Auszeischnung). <br />- In 2008, was honored with the selection as a testimonial in the Postgraduate & Doctoral Education by the International School for Graduate Studies at the University of Kaiserslautern/ Germany <br />- PATENT: System and method for simulating and modelling the distribution of discrete systems, United States Patent Application: 0100106467)edit - Hans-Jörg Bartedit
Adsorption cooling is a promising technology to recover low-temperature waste heat from a diesel genset. In this paper, an advanced adsorption chiller working in variable mode is proposed for the combined cooling and power cycle (CCP) to... more
Adsorption cooling is a promising technology to recover low-temperature waste heat from a diesel genset. In this paper, an advanced adsorption chiller working in variable mode is proposed for the combined cooling and power cycle (CCP) to recover waste heat from the water jacket in the diesel genset. The chiller works on three modes based on the ambient temperature for better heat utilization. In this study, three modes were investigated: single-stage cycle mode, short-duration, and medium-duration mass recovery modes. The results show that the energy and exergy efficiency for a single-stage cycle mode is higher at an ambient temperature lower than 35 °C . In comparison, the mass recovery mode has a higher energy and exergy efficiency at an ambient temperature higher than 35 °C. The annual energy and exergy efficiency for the CCP was investigated when the chiller works with variable modes based on the ambient temperature under DUBAI weather conditions as a case study. The results sho...
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Adsorption cooling can recover waste heat at low temperature levels, thereby saving energy and reducing greenhouse gas emissions. An air-cooled adsorption cooling system reduces water consumption and the technical problems associated with... more
Adsorption cooling can recover waste heat at low temperature levels, thereby saving energy and reducing greenhouse gas emissions. An air-cooled adsorption cooling system reduces water consumption and the technical problems associated with wet-cooling systems; however, it is difficult to maintain a constant recooling water temperature using such a system. To overcome this limitation, a variable mode adsorption chiller concept was introduced and investigated in this study. A prototype adsorption chiller was designed and tested experimentally and numerically using the lumped model. Experimental and numerical results showed good agreement and a similar trend. The adsorbent pairs investigated in this chiller consisted of silicoaluminophosphate (SAPO-34)/water. The experimental isotherm data were fitted to the Dubinin–Astakhov (D–A), Freundlich, Hill, and Sun and Chakraborty (S–C) models. The fitted data exhibited satisfactory agreement with the experimental data except with the Freundlic...
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We conducted energy and exergy analyses of an adsorption chiller to investigate the effect of recooling-water temperatures on the cooling capacity and Coefficient of Performance (COP) with variable cycle modes. We investigated both the... more
We conducted energy and exergy analyses of an adsorption chiller to investigate the effect of recooling-water temperatures on the cooling capacity and Coefficient of Performance (COP) with variable cycle modes. We investigated both the effect of the recooling-water temperature and the dead state temperature on the exergy destruction in the chiller components. Our results show that there is an optimum reheat cycle mode for each recooling-water temperature range. For the basic single stage cycle, the exergy destruction is mainly accrued in the desorber (49%), followed by the adsorber (27%), evaporator (13%), condenser (9%), and expansion valve (2%). The exergy destruction for the preheating process is approximately 35% of the total exergy destruction in the desorber. By contrast, the precooling process is almost 58% of the total exergy destruction in the adsorber. The exergy destruction decreases when increasing the recooling-water and the dead state temperatures, while the exergy eff...
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ABSTRACT Abstract A hierarchical approach for modelling and simulation of coupled hydrodynamics and mass transfer in liquid extraction columns using detailed and reduced bivariate population balance models is presented. The hierarchical... more
ABSTRACT Abstract A hierarchical approach for modelling and simulation of coupled hydrodynamics and mass transfer in liquid extraction columns using detailed and reduced bivariate population balance models is presented. The hierarchical concept utilizes a one-dimensional CFD model with detailed bivariate population balances. This population balance model is implemented in the PPBLAB software, which is used to optimize the column hydrodynamics. The optimized droplet model parameters (droplet breakage and coalescence) are then used by a two-dimensional CFD reduced population balance model. As a reduced bivariate population balance model, OPOSPM (One Primary and One Secondary Particle Method) is implemented in the commercial FLUENT software to predict the coupled hydrodynamics and mass transfer of an RDC extraction column with 88 compartments. The simulation results show that the coupled two-dimensional-OPOSPM model produces results that are very close to that of the one-dimensional PPBLAB detailed population balance model. The advantages of PPBLAB are the ease of model setup, implementation and the reduced simulation time (order of minutes), when compared to the computational time (order of weeks) and computational resources using FLUENT software. The advantages of the two-dimensional CFD model is the direct estimation of the turbulent energy dissipation using the k-ε model and the local resolution of continuous phase back mixing.
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In this work, computational fluid dynamics (CFD) calculations coupled with DPBM are compared to LLECMOD (Liquid-Liquid Extraction Column MODule) simulations and to Laser Induced Fluorescence (LIF) measurement of the phase fraction using... more
In this work, computational fluid dynamics (CFD) calculations coupled with DPBM are compared to LLECMOD (Liquid-Liquid Extraction Column MODule) simulations and to Laser Induced Fluorescence (LIF) measurement of the phase fraction using an iso-optical system of calcium chloride/water and butyl acetate. The results show a good agreement between the simulations and experimental data. The CFD requires a high computational load
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Research Interests: Mechanical Engineering, Chemical Engineering, Mathematics, Numerical Simulation, Liquid Liquid Extraction, and 15 moreCase Study, PARTIAL DIFFERENTIAL EQUATION, Steady state, Spatial Distribution, Historic conservation law, Second Order, Time Dependent, Continuous Flow, Chemical Engineering Science, Population Balance Equation, Numerical Solution, Spatial Dependence, discrete model, Upwind Scheme, and Operator Splitting (Case Study, PARTIAL DIFFERENTIAL EQUATION, Steady state, Spatial Distribution, Historic conservation law, Second Order, Time Dependent, Continuous Flow, Chemical Engineering Science, Population Balance Equation, Numerical Solution, Spatial Dependence, discrete model, Upwind Scheme, and Operator Splitting )
(Case Study, PARTIAL DIFFERENTIAL EQUATION, Steady state, Spatial Distribution, Historic conservation law, Second Order, Time Dependent, Continuous Flow, Chemical Engineering Science, Population Balance Equation, Numerical Solution, Spatial Dependence, discrete model, Upwind Scheme, and Operator Splitting )
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For the design of counter-current liquid–liquid extraction columns, there is a strong industrial demand for more straightforward, faster and money-saving simulation methods. One possibility in this direction that has a great potential is... more
For the design of counter-current liquid–liquid extraction columns, there is a strong industrial demand for more straightforward, faster and money-saving simulation methods. One possibility in this direction that has a great potential is the coupling of computational fluid dynamics (CFD) with population balance models (PBM). Therefore, a combination of CFD and droplet population balance modelling (DPBM) is applied to simulate
Research Interests: Chemical Engineering, Design, Computational Fluid Dynamics, Conception, Dispersion, and 15 moreComputation Fluid Dynamics, Bubble, Bubble Column, Discretization, Droplet, Design Tool, EXTRACTION, Chemical Engineering Science, DROP, Experimental Measurement, Coalescence, Drop Size Distribution, Droplet Size Distribution, Droplet Size, and Euler Equation
ABSTRACT Modeling and dynamic analysis of liquid extraction columns are essential for the design, control strategies and understanding of column behavior during start up and shutdown. Because of the discrete character of the dispersed... more
ABSTRACT Modeling and dynamic analysis of liquid extraction columns are essential for the design, control strategies and understanding of column behavior during start up and shutdown. Because of the discrete character of the dispersed phase, the population balance modeling framework is needed. Due to the mathematical complexity of the full population balance model, it is still not feasible for dynamic and online control purposes. In this work, a reduced mathematical model is developed by applying the concept of the primary and secondary particle method (Attarakih et al., 2009b, Solution of the population balance equation using the one primary and one secondary particle method (OPOSPM), Computer Aided Chemical Engineering, vol. 26, pp. 1333–1338). The method is extended to solve the nonhomogenous bivariate population balance equation, which describes the coupled hydrodynamics and mass transfer in an RDC extraction column. The model uses only one primary and one secondary particles, which can be considered as Lagrangian fluid particles carrying information about the distribution as it evolves in space and time. This information includes averaged quantities such as total number, volume and solute concentrations, which are tracked directly through a system of coupled hyperbolic conservation laws with nonlinear source terms. The model describes droplet breakage, coalescence and interphase solute transfer. Rigorous hyperbolic analysis of OPOSPM uncovered the existence of four waves traveling along the column height. Three of these are contact waves, which carry volume and solute concentration information. The dynamic analysis in this paper reveals that the dominant time constant is due to solute concentration in the continuous phase. On the other hand, the response of the dispersed phase mean properties is relatively faster than the solute concentration in the continuous phase. Special shock capturing method based on the upwind scheme with flux vector splitting is used, with explicit wave speeds, as a time–space solver. The model shows a good match between analytical and numerical results for special steady state and dynamic cases as well as the published steady state experimental data.
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Research Interests: Mechanical Engineering, Chemical Engineering, Chemistry, Mass Transfer, Density-functional theory, and 12 moreSimulation, Liquid Liquid Extraction, Density Functional Theory, Interfacial Tension, Hydrodynamics, Spatial Distribution, Breakage, Chemical Engineering Science, Population Balance Equation, Experimental Validation, Numerical Solution, and Coalescence
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Research Interests: Mechanical Engineering, Chemical Engineering, Mathematics, Applied Mathematics, Modeling, and 11 moreDiscretization, Gaussian quadrature, Spatial Distribution, EXTRACTION, Nystrom method, Finite Difference, Interdisciplinary Engineering, Population Balance Equation, COLUMNS, Chemical Engineering Technology, and Bivariate Analysis
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The simulation of liquid–liquid extraction columns based on a droplet population balance approach provides a useful means for getting more insight into the transient and the steady state behavior of such an extremely important unit... more
The simulation of liquid–liquid extraction columns based on a droplet population balance approach provides a useful means for getting more insight into the transient and the steady state behavior of such an extremely important unit operation. This numerical simulation is carried out based on a recently developed algorithm for solving the population balance equation. The algorithm is implemented via a
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The population balance equation finds many applications in modelling poly-dispersed systems arising in many engineering applications such as aerosols dynamics, crystallization, precipitation, granulation, liquid-liquid, gas-liquid,... more
The population balance equation finds many applications in modelling poly-dispersed systems arising in many engineering applications such as aerosols dynamics, crystallization, precipitation, granulation, liquid-liquid, gas-liquid, combustion processes and microbial systems. The population balance lays down a modern approach for modelling the complex discrete behaviour of such systems. Due to the industrial importance of liquid-liquid extraction columns for the separation of many chemicals that are not amenable for separation by distillation, a Windows based program called LLECMOD is developed. Due to the multivariate nature of the population of droplets in liquid –liquid extraction columns (with respect to size and solute concentration), a spatially distributed population balance equation is developed. The basis of LLECMOD depends on modern numerical algorithms that couples the computational fluid dynamics and population balances. To avoid the solution of the momentum balance equat...
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Abstract In this work, we present a new population balance based module for modelling the hydrodynamics and mass transfer processes in pulsed packed bed liquid extraction columns. The new module is fully implemented using PPBLab software,... more
Abstract
In this work, we present a new population balance based module for modelling the hydrodynamics and mass transfer processes in pulsed packed bed liquid extraction columns. The new module is fully implemented using PPBLab software, which utilizes recent population balance model solution algorithms. In this regard, the PPBLab detailed and reduced extended fixed pivot solvers are used to discretize the internal coordinates, while the PPBLab built-in space-time solver is used to discretize the physical spatial domain. In addition to this, a user-friendly interface is designed to facilitate the user inputs and outputs and to allow a full access to the CAPE-OPEN thermodynamics package (TEA). As a case study, this PPBLab column module is validated using the published steady state experimental data for water-acetone-toluene chemical system in a DN80 pulsed packed bed liquid extraction column. The predicted column performance is found to agree well with PPBLab software simulation results.
Keywords
Population balances; Mathematical modelling; PPBLab; Pulsed packed column; CAPE-OPEN
In this work, we present a new population balance based module for modelling the hydrodynamics and mass transfer processes in pulsed packed bed liquid extraction columns. The new module is fully implemented using PPBLab software, which utilizes recent population balance model solution algorithms. In this regard, the PPBLab detailed and reduced extended fixed pivot solvers are used to discretize the internal coordinates, while the PPBLab built-in space-time solver is used to discretize the physical spatial domain. In addition to this, a user-friendly interface is designed to facilitate the user inputs and outputs and to allow a full access to the CAPE-OPEN thermodynamics package (TEA). As a case study, this PPBLab column module is validated using the published steady state experimental data for water-acetone-toluene chemical system in a DN80 pulsed packed bed liquid extraction column. The predicted column performance is found to agree well with PPBLab software simulation results.
Keywords
Population balances; Mathematical modelling; PPBLab; Pulsed packed column; CAPE-OPEN
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We present a continuous approximation to the population balance equation which has few analytical solutions that are only of academic interest. The proposed solution is a stable and well-conditioned converging sequence of continuous... more
We present a continuous approximation to the population balance equation which has few analytical solutions that are only of academic interest. The proposed solution is a stable and well-conditioned converging sequence of continuous approximations to the number concentration function. Instead of using the moments of the number concentration function as constraints when applying the Maximum Entropy (MaxEnt) method, we require the MaxEnt functional to satisfy pointwise local information sampled from the number concentration function. The solution of this constrained optimization problem results in a continuous Lagrange multiplier which is then expanded using a complete set of orthogonal Chebyshev basis functions. The coefficients of the expansion are then derived in a closed form using local information about the number concentration function. As an application, the present method is validated using an analytical solutions of additive particle aggregation frequency plus first-order particle depletion rate and steady state particle breakage in a continuous homogeneous flow system. The method is found to produce comparable results to that predicted by the Chebyshev-QMOM as the pointwise local information is increased.
Keywords
Population balances; Maximum Entropy Method; Orthogonal Expansion
Keywords
Population balances; Maximum Entropy Method; Orthogonal Expansion
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A reduced steady state population balance model, based on the Spatially Mixed-Sectional Quadrature Method Of Moments (SM-SQMOM), is developed to model the reactive extraction process of zinc with D2EHPA in a Kühni liquid-liquid extraction... more
A reduced steady state population balance model, based on the Spatially Mixed-Sectional Quadrature Method Of Moments (SM-SQMOM), is developed to model the reactive extraction process of zinc with D2EHPA in a Kühni liquid-liquid extraction column. The numerical flux vectors of the hydrodynamic transport equations are closed using one quadrature point, where an analytical solution based on the algebraic velocity model is used to calculate the required dispersed phase mean droplet velocity along the column height. In addition to this, a multi-sectional grid (w.r.t. droplet diameter) is used to approximate the source terms of the hydrodynamic transport equations, while one section (w.r.t. droplet solute concentration) is used to model the steady state reactive mass transfer behavior inside the column. The proposed model is validated with the experimental data using ZnSO4/D2EHPA in isododecane EFCE chemical test system. The effect of changing the rotational speed, phase ratio and the total throughput on the column performance is investigated. The SM-SQMOM is found able to reconstruct the shape of the droplet size distribution and to predict the zinc reactive concentration profiles along the column height as compared with the experimental data.
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Liquid-liquid extraction columns have a small footprint, a high number of theoretical stages and allow high throughput. However, the deviation of the flow field from the ideal plug flow makes the simulation and design of these columns a... more
Liquid-liquid extraction columns have a small footprint, a high number of theoretical stages and allow high throughput. However, the deviation of the flow field from the ideal plug flow makes the simulation and design of these columns a challenging task. In order to help in this tedious design procedure (scale-up experiments) two simulation tools are presented. The first one is the PPBLAB software, which is based on a one-dimensional CFD (Computational Fluid Dynamics) model. Deviations from the ideal plug flow are accounted by the axial dispersion and by population balance modeling, which accounts for the droplet-droplet interactions and forward mixing of the dispersed phase. The second tool is based on a three dimensional modelling of the flow field using 3D CFD simulation, which is able to describe the local flow field without any geometrical dependent correlations more than the drag coefficient correlation. As a case study, a Kühni mini-plant column is simulated using the one dimensional and the three dimensional tools for comparison. The design procedure of each tool is shown, where the benefits (computational time, local information) of each tool are highlighted.
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In this work, the Sectional Quadrature Method Of Moments (SQMOM) is extended to solve the nonhomogeneous population balance equation along the spatial domain to model the hydrodynamics and mass transfer behaviour of liquid-liquid... more
In this work, the Sectional Quadrature Method Of Moments (SQMOM) is extended to solve the nonhomogeneous population balance equation along the spatial domain to model the hydrodynamics and mass transfer behaviour of liquid-liquid extraction columns. The required quadrature nodes and weights are calculated analytically using the Two-Equal Weight Quadrature (TEqWQ) formula derived by Attarakih et al., (Attarakih, M., Drumm, C., & Bart, H.-J., (2009), Solution of the population balance equation using the Sectional Quadrature Method of Moments (SQMOM). Chem. Eng. Sci., 64, 742-752). As a numerical test, the SQMOM was validated using PPBLab software which utilizes the detailed extended fixed pivot as a built-in solver. Moreover, the SQMOM was experimentally validated using the available published steady state experimental data for both chemical test systems: Water-acetone-toluene and water-acetone-butyl acetate chemical test systems for RDC DN80 liquid extraction column.
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Bubbly gas flow in vertical tubes received considerable attention due to its applications in chemical, biochemical industries and nuclear reactor design and safety consideration. The use of CFD is called for to avoid the dependence of... more
Bubbly gas flow in vertical tubes received considerable attention due to its applications in chemical, biochemical industries and nuclear reactor design and safety consideration. The use of CFD is called for to avoid the dependence of steady state operation and accident analysis on empirical correlations. This is due to the dependence of these correlations on flow regimes, scaling and geometrical factors. The situation becomes more complicated when the gas bubble-bubble and bubble-continuous phase interactions are taken into account in which bubble growth, breakage and coalescence could not be neglected. In such cases, the application of the two-fluid bubbly flow model becomes limited where only bubble expansion is be taken into account. In this contribution, we bridged the gap between the bubbly flow two-fluid model and the population balances by introducing the OPOSPM as a consistent and reduced population balance model. This adds an extra degree of details by considering the instantaneous bubble breakage and coalescence in the source term of the total bubble number concentration transport equation. The 2D CFD-OPOSPM model was validated against published experimental data of bubbly flow in vertical tubes.
This work presents a new windows-based MATLAB program, which is called PPBLAB (Particulate Population Balance Laboratory) for modelling and numerical simulation of particulate systems. As a first step, liquid-liquid extraction columns are... more
This work presents a new windows-based MATLAB program, which is called PPBLAB (Particulate Population Balance Laboratory) for modelling and numerical simulation of particulate systems. As a first step, liquid-liquid extraction columns are modelled using the population balance equation as a mathematical framework. Up to date population balance models and solvers are incorporated. The discretization of the spatial domain is based on the finite volume method with flux vector splitting. A strongly stable semi-implicit first order time integration scheme is used to resolve such a large and stiff ODE system. The MATLAB GUI is used to make PPBLAB a user friendly program, which allows the user to define and simulate liquid extraction columns. A thermodynamics package TEA-COCO, which obtained from CAPE-OPEN, is linked to PPBLAB. Therefore, a special interface is designed for the purpose of data exchange between PPBLAB and CAPE-OPEN TEA tool. The solute distribution coefficient in ternary systems is predicted using the UNIQUAC model with a special optimization tool to estimate the binary interaction parameters based on infinite conditions. A pilot plant Kühni extraction column is simulated and tested. Full analysis and performance of the PPBLAB are carried out and validated against experimental data.
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Various particulate systems were modeled by the population balance equation (PBE). However, only few cases of analytical solutions for the breakage process do exist, with most solutions being valid for the batch stirred vessel. The... more
Various particulate systems were modeled by the population balance equation (PBE). However, only few cases of analytical solutions for the breakage process do exist, with most solutions being valid for the batch stirred vessel. The analytical solutions of the PBE for particulate processes under the influence of particle breakage in batch and continuous processes were investigated. Such solutions are obtained from the integro-differential PBE governing the particle size distribution density function by two analytical approaches: the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM). ADM generates an infinite series which converges uniformly to the exact solution of the problem, while HPM transforms a difficult problem into a simple one which can be easily handled. The results indicate that the two methods can avoid numerical stability problems which often characterize general numerical techniques in this area.
The breakage in batch and continuous systems has attained high interest in chemical engineering and granulation from a process and from a product quality perspective. The wet granule breakage process in a high shear mixer will influence... more
The breakage in batch and continuous systems has attained high interest in chemical engineering and granulation from a process and from a product quality perspective. The wet granule breakage process in a high shear mixer will influence and may control the final granule size distribution. In this work, we developed analytical solutions of the particle breakage using the population balance equation (PBEs) in batch and continuous flow systems. To allow explicit solutions, we approximate particle breakage mechanisms with assumed functional forms for breakage frequencies. This new framework for solving (PBEs) for batch and continuous flow systems proposed in this work uses the Adomian decomposition method (ADM) and the variational iteration method (VIM). These semi-analytical methods overcome the crucial difficulties of numerical discretization and stability that often characterize previous solutions in of the PBEs. The results obtained in all cases show that the predicted particle size distributions converge exactly in a continuous form to that of the analytical solutions using the two methods.
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In this work, the number density function in the population balance equation (PBE) is approximated in terms of field nodes through a complete set of orthogonal basis functions in a semi-logarithmic space. We proposed the functional values... more
In this work, the number density function in the population balance equation (PBE) is approximated in terms of field nodes through a complete set of orthogonal basis functions in a semi-logarithmic space. We proposed the functional values at these field nodes to satisfy the maximum entropy solution. This hybridization of function approximation and information theories based on Shannon Maximum Entropy principle, allowed us to construct a sequence of positive continuous approximations of the PBE. The Lagrange multipliers, which result from the maximization of the Shannon entropy subject to the available average information, was estimated by solving a well-conditioned linear system of algebraic equations. As an application, this meshfree solution of the PBE is validated using an analytical solution of the microbial cell dynamics in a constant abiotic environment with simultaneous cell growth and division for which the analytical solution was derived by using the Adomian method.
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Dynamic behaviour, control and design strategies for liquid extraction equipment are faced by the complex hydrodynamic behavior of the dispersed phase with many droplet interactions (e.g. breakage and coalescence). To take this into... more
Dynamic behaviour, control and design strategies for liquid extraction equipment are faced by the complex hydrodynamic behavior of the dispersed phase with many droplet interactions (e.g. breakage and coalescence). To take this into account, the population balance modelling framework is used by implementing the bivariate OPOSPM (One Primary and One Secondary Particle Method) with a one-dimensional finite volume method in the physical space. To narrow the gap between the steady state and dynamic design during process synthesis, OPOSPM is implemented in a MATLAB/Simulink flowsheeting environment. As an outcome of this, we present a new OPOSPM-MATLAB/Simulink module which is called OPOSSIM for modeling and simulation the coupled two-phase flow and mass transfer in a Kuhni liquid extraction column.
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In this contribution, we used a reduced population balance model to describe the hydrodynamics of bubble columns, which play a major role in in determining the bubble size distribution and hence the interfacial area concentration. This... more
In this contribution, we used a reduced population balance model to describe the hydrodynamics of bubble columns, which play a major role in in determining the bubble size distribution and hence the interfacial area concentration. This model consists of a set of transport equations to track the total number and total interfacial area concentrations and the gas phase volume fraction of bubbles. The model is essentially derived using the One Primary and One Secondary Particle Method (OPOSPM) and its higher extension using an Implicit Two-Equal Weight Quadrature (TwoEqWQ). This is coupled with the Shannon Maximum Entropy Method to predict the bubble size distribution along the bubble column axial direction. The model predictions show good agreement with the published experimental data in the bubbly flow regime.
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A hierarchical approach for modeling and simulation of coupled hydrodynamics and mass transfer in liquid extraction columns using detailed and reduced bivariate population balance models is presented. The hierarchical concept utilizes a... more
A hierarchical approach for modeling and simulation of coupled hydrodynamics and mass transfer in liquid extraction columns using detailed and reduced bivariate population balance models is presented. The hierarchical concept utilizes a one-dimensional CFD model with detailed bivariate population balances. This population balance model is implemented in the PPBLAB software which is used to optimize the column hydrodynamics. The optimized droplet model parameters (droplet breakage and coalescence) are then used by a two-dimensional CFD reduced population balance model. As a reduced bivariate population balance model, OPOSPM (One Primary and One Secondary Particle Method) is implemented in the commercial FLUENT software to predict the coupled hydrodynamics and mass transfer of an RDC extraction column with 88 compartments. The simulation results show that the coupled two-dimensional-OPOSPM model produces results that are very close to that of the one-dimensional PPBLAB detailed population balance model. The advantages of PPBLAB are the ease of model setup, implementation and the reduced simulation time (order of minutes), when compared to the computational time (order of weeks) and computational resources using FLUENT software. The advantages of the two-dimensional CFD model is the direct estimation of the turbulent energy dissipation using the k–ε model and the local resolution of continuous phase back mixing.
Research Interests:
The population balance equation (PBE) is an integro-partial differential equation with nonlinear source term. The PBE is known to admit analytical solutions only for a few cases with restricted forms of interaction kernels. We propose for... more
The population balance equation (PBE) is an integro-partial differential equation with nonlinear source term. The PBE is known to admit analytical solutions only for a few cases with restricted forms of interaction kernels. We propose for the first time a novel converging sequence of continuous approximations to the number concentration function as a solution to the population balance equation (PBE). These approximations are internally consistent with respect to any finite number of desired moments. The uniqueness and convergence of such a sequence are assured by being an optimal solution to the constrained NLP, which maximizes the constrained Shannon entropy function. The solution is an optimal functional containing the maximum missed information about the distribution. This entropy maximization problem is a convex program and is solved by converting the constrained NLP into a set of transport equations in terms of the optimal Lagrange multipliers. Since differential form of the Lagrange multipliers is used, the method is given the name the Differential Maximum Entropy (DMaxEnt) method. The DMaxEnt method is tested using many standard and even complex liquid–liquid extraction processes, where the population balance modeling is needed.
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The population balance equation for particle growth finds many applications in chemical process industries and physical sciences. It is a hyperbolic partial differential with few known analytical solutions. We propose in this paper a... more
The population balance equation for particle growth finds many applications in chemical process industries and physical sciences. It is a hyperbolic partial differential with few known analytical solutions. We propose in this paper a novel converging sequence of continuous approximations to this equationfor the case of one- and two- dimensional particle growth. The uniqueness and convergence of such a sequence are assured by maximizing the Shannon entropy function, which is associated witha set of Lagrange multipliers. In contrast to the classical Maximum Entropy Method (MaxEntM), the Lagrange multipliers are estimated using a meshless method by point wise sampling of the continuous distribution. The proposed method provides local information about this distribution and is consistent with its low-order moments
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Modeling and dynamic analysis of liquid extraction columns are essential for the design, control strategies and understanding of column behavior during start up and shutdown. Because of the discrete character of the dispersed phase, the... more
Modeling and dynamic analysis of liquid extraction columns are essential for the design, control strategies and understanding of column behavior during start up and shutdown. Because of the discrete character of the dispersed phase, the population balance modeling framework is needed. Due to the mathematical complexity of the full population balance model, it is still not feasible for dynamic and online control purposes. In this work, a reduced mathematical model is developed by applying the concept of the primary and secondary particle method (Attarakih et al., 2009b, Solution of the population balance equation using the one primary and one secondary particle method (OPOSPM), Computer Aided Chemical Engineering, vol. 26, pp. 1333–1338). The method is extended to solve the nonhomogenous bivariate population balance equation, which describes the coupled hydrodynamics and mass transfer in an RDC extraction column. The model uses only one primary and one secondary particles, which can be considered as Lagrangian fluid particles carrying information about the distribution as it evolves in space and time. This information includes averaged quantities such as total number, volume and solute concentrations, which are tracked directly through a system of coupled hyperbolic conservation laws with nonlinear source terms. The model describes droplet breakage, coalescence and interphase solute transfer. Rigorous hyperbolic analysis of OPOSPM uncovered the existence of four waves traveling along the column height. Three of these are contact waves, which carry volume and solute concentration information. The dynamic analysis in this paper reveals that the dominant time constant is due to solute concentration in the continuous phase. On the other hand, the response of the dispersed phase mean properties is relatively faster than the solute concentration in the continuous phase. Special shock capturing method based on the upwind scheme with flux vector splitting is used, with explicit wave speeds, as a time–space solver. The model shows a good match between analytical and numerical results for special steady state and dynamic cases as well as the published steady state experimental data.
Research Interests:
Numerical solution of the population balance equation (PBE) is widely used in many scientific and engineering applications. Available numerical methods, which are based on tracking population moments instead of the distribution, depend on... more
Numerical solution of the population balance equation (PBE) is widely used in many scientific and engineering applications. Available numerical methods, which are based on tracking population moments instead of the distribution, depend on quadrature methods that destroy the distribution itself. The reconstruction of the distribution from these moments is a well-known ill-posed problem and still unresolved question. The present integral formulation of the PBE comes to resolve this problem. As a closure rule, a Cumulative QMOM (CQMOM) is derived in terms of the monotone increasing cumulative moments of the number density function, which allows a complete distribution reconstruction. Numerical analysis of the method show two unique properties: first, the method can be considered as a mesh-free method. Second, the accuracy of the targeted low-order cumulative moments depends only on order of the CQMOM, but not on the discrete grid points used to sample the cumulative moments.
First Term 2014/2015
Mid Exam, Short & Full Reports
Mean: 33.00
STD: 6.00
Number of Students: 23
Mid Exam, Short & Full Reports
Mean: 33.00
STD: 6.00
Number of Students: 23
First Term 2014/2015
Mid Exams, Project & Presentation
Mean: 27.16
STD: 6.10
Number of Students: 25
Mid Exams, Project & Presentation
Mean: 27.16
STD: 6.10
Number of Students: 25
First Term 2014/2015
Mid Exams, Project & Presentation
Mean: 25.58
STD: 7.70
Number of Students: 50
Mid Exams, Project & Presentation
Mean: 25.58
STD: 7.70
Number of Students: 50