Process systems modelling and applications in granulation: A review

Cameron, Ian; Wang, F.Y.; Immanuel, Charles D.; Štěpánek, František

doi:10.1016/j.ces.2005.02.004

Cited by 152 publications

(83 citation statements)

References 65 publications

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“…Multiscale modelling approach basically consists of the division of a complex problem/model into a set of sub-problems/models that are described at different scales of length or/and time, in order to improve the degree of details of the phenomena that the set of mathematical model is describing in product-process design. Furthermore, multiscale approach facilitates the discovery and manufacture of complex products (Cameron et al, 2005); it is possible to observe that two different scales are involved: mesoscale and micro-scale. The meso-scale involves the modelling of the anode and cathode compartments while the micro-scale is employed to model, the behaviour of the anode and cathode catalyst layers and the proton membrane exchange.…”

Section: Fig 7 Icas-mot Cape-open Unit Operationmentioning

confidence: 99%

Interoperability between Modelling Tools (MoT) with Thermodynamic Property Prediction Packages (Simulis® Thermodynamics) and Process Simulators (ProSimPlus) via CAPE-OPEN Standards

Morales-Rodríguez¹,

Gani²,

Déchelotte³

et al. 2011

Thermodynamics

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Thermodynamics 426both traditional and internet-based mechanism; assessment of the use and benefits of CAPE-OPEN standards for educations and training (Braunschweig et al., 2000). Currently, several commercial simulator vendors, modelling tools developers, etc. have incorporated CAPE-OPEN standard in their products, allowing the user a better and easier manner for implementation/combination among process modelling components (PMC) and process modelling environments (PME) (Pons, 2003). CAPE-OPEN is an abstract specification that can be subsequently implemented in COM, CORBA and .NET for bridging PMCs and PMEs. Recently, .NET framework has been introduced as a new alternative to provide the interoperability among different platforms. This new technology has been presented by Microsoft and it seems to be visualized as the future of the connections between different platforms. CO-LaN has published guidelines on how to use .NET with CAPE-OPEN, this is available in CO-LaN website at http://www.colan.org/News/Y06/news-0616.htm. In this chapter, a connection between a modelling tool (ICAS-MoT) representing a PMC and external simulators (ProSimPlus and Simulis® Thermodynamics) representing a PME is established and implemented through the CAPE-OPEN standards and highlighted through two case studies. The interoperability issues of ICAS-MoT and Simulis® Thermodynamics are highlighted through case study number one. Here, a thermodynamic property model is generated by ICAS-MoT and wrapped to satisfy the CAPE-OPEN standard. A second case study highlights the interaction issues between ICAS-MoT and ProSimPlus regarding the use of a non-conventional unit operation (model generated in ICAS-MoT) plugged to the ProSimPlus simulator environment. Furthermore, as this unit operation model is employing a multiscale modelling approach, these issues are also highlighted through the case study.

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Section: Fig 7 Icas-mot Cape-open Unit Operationmentioning

confidence: 99%

Interoperability between Modelling Tools (MoT) with Thermodynamic Property Prediction Packages (Simulis® Thermodynamics) and Process Simulators (ProSimPlus) via CAPE-OPEN Standards

Morales-Rodríguez¹,

Gani²,

Déchelotte³

et al. 2011

Thermodynamics

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“…The numerical solution of a population balance equation (PBE) is highly demanded in many industrial applications such as crystallization, polymerization etc., see for example [3,25,26]. The PBE depends not only on time and space but also contains derivatives with respect to the properties of the particles (internal variables) such as the size, length, etc.…”

Section: Introductionmentioning

confidence: 99%

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

Ganesan

2012

ESAIM: M2AN

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Abstract. We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.Mathematics Subject Classification. 35K20, 65M60, 65M12.

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“…[1,2] Population balance models (PBMs) have provided such an interface which connects the different scales and deals with several particulate processes simultaneously. [3,4] Population balance modelling is a very useful tool in chemical engineering. [5] It has diverse applications including polymerization, crystallization, precipitation, and several other chemical industrial processes.…”

Section: Introductionmentioning

confidence: 99%

Population balances in case of crossing characteristic curves: Application to T‐cells immune response

Ali

Elkamel

Gruy³

et al. 2016

Can J Chem Eng

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The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, mass, and protein concentration) is typically modelled by a population balance equation, a first-order linear hyperbolic partial differential equation that is shared by all T-cells is involved. At these crossing points, the linear advection equation is not possible by using the hyperbolic conservation laws in a classical way. Therefore, a new transport method is introduced in this article that is able to find the population density function for such processes. A multi-scale mathematical modelling framework is employed. At the first scale, two processes, which are termed as the activation and reaction terms (assimilated as nucleation and growth in chemical processes), are studied as independent processes. At the second scale, the dynamic variation in the population density of activated T-cells is investigated in the presence of activation and reaction terms. The newly-developed transport method is shown to work in the case of crossing and to provide a smooth solution at the crossing points in contrast to the classical PDF techniques.2

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Process systems modelling and applications in granulation: A review

Cited by 152 publications

References 65 publications

Interoperability between Modelling Tools (MoT) with Thermodynamic Property Prediction Packages (Simulis® Thermodynamics) and Process Simulators (ProSimPlus) via CAPE-OPEN Standards

Interoperability between Modelling Tools (MoT) with Thermodynamic Property Prediction Packages (Simulis® Thermodynamics) and Process Simulators (ProSimPlus) via CAPE-OPEN Standards

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

Population balances in case of crossing characteristic curves: Application to T‐cells immune response

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