The OPOSPM as a Nonlinear Autocorrelation Population Balance Model for Dynamic Simulation of Liquid Extraction Columns

Attarakih, Menwer; Jildeh, Hanin B.; Mickler, Matthias; Bart, Hans‐Jörg

doi:10.1016/b978-0-444-59506-5.50074-2

Cited by 18 publications

(15 citation statements)

References 4 publications

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“…The interaction parameters in the breakage and coalescence kernels in Equation are derived using the inverse detailed population balance model (CM‐PBM), with the correlation parameters, b i and c i , in the two kernels taken from Table . This serves as the basis for the learning parameters K b and K c in Equation in OPOSPM, using a weighted nonlinear least square optimisation with simple bounds . The optimisation is done for a column (see Table ) with an internal diameter of 150 mm, 1400 mm height, seven compartments and dispersed phase inlet at 0.15 and 0.90 m for continuous phase, which gives K b = 1.400 and K c = 2.515 being in agreement to published data …”

Section: Resultssupporting

confidence: 71%

“…For online prediction and reduction purposes, the model has been simplified and adjusted by introducing two learning parameters ( K b and K c ) for the breakage and coalescence kernels, respectively . Based on this modification the source term in Equation is given by:

S = K_{b} (ϑ (d_{30}) - 1) Γ (d_{30}) N - \frac{1}{2} K_{c} ω (d_{30}, d_{30}) N^{2}

…”

Section: Droplet Population Balancementioning

confidence: 99%

“…An alternative approach, which is faster and computationally less expensive, is the use of learning parameters, during online experiments . In the learning phase, data is used for parameter optimisation.…”

Section: Introductionmentioning

confidence: 99%

“…In the learning phase, data is used for parameter optimisation. This requires a fast and simple PBM, as is the One Primary and One Secondary Particle Method (OPOSPM), which was proposed by Attarakih et al The so retrieved optimised learning parameters can be used for column simulation and control …”

Section: Introductionmentioning

confidence: 99%

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Parameter optimisation and validation for droplet population balances

et al. 2013

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Single droplet experiments in Kühni compartment for five different liquid systems were used to evaluate Schmidt breakage model parameters. Based on these optimised parameters, Coulaloglou and Tavlarides coalescence model parameters were obtained by an inverse solution of population balance model (PBM) using the extended fixed‐pivot technique. The estimated interaction parameters were used to study the hydrodynamics of a pilot Kühni column. For online prediction purposes the One Primary and One Secondary Particle Model (OPOSPM), which is essentially a reduced population balance model (PBM), was used as an alternative to the computational expensive detailed PBM. Different test systems and column geometries were used for steady and transient state validation where OPOSPM was found to produce remarkable good results.

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Section: Resultssupporting

confidence: 71%

S = K_{b} (ϑ (d_{30}) - 1) Γ (d_{30}) N - \frac{1}{2} K_{c} ω (d_{30}, d_{30}) N^{2}

…”

Section: Droplet Population Balancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parameter optimisation and validation for droplet population balances

et al. 2013

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“…It is the simplest discrete model that can approximate the continuous population balance equation . It uses the primary and secondary particle concept, where the primary particles are responsible for the reconstruction of the distribution and the secondary particle to describe the particle interactions (breakage or coalescence) . The number balance is:

\frac{\partial N}{\partial t} + \frac{\partial (u_{normaly} N)}{\partial z} = \frac{1}{A_{normalc}} \frac{Q_{normaly}^{in}}{v_{in}} δ (z - z_{normaly}) + S

and the volume balance results in:

\frac{\partial α}{\partial t} + \frac{\partial (u_{y} α)}{\partial z} = \frac{Q_{normaly}^{in}}{A_{normalc}} δ (z - z_{normaly})

The model conserves the total number ( N ) and volume ( α ) concentrations of the population by solving directly two transport equations for N and α in time and space.…”

Section: Simulation and Prediction Methodsmentioning

confidence: 99%

Online monitoring, simulation and prediction of multiphase flows

et al. 2013

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An online monitoring and simulation tool (OMST) is used to determine, analyse, simulate and predict the multiphase flow behaviour in an extraction column within the context of model predictive control (MPC). The simulation was done with the droplet population model OPOSPM using an adapted moments method for online simulation. For validation, steady‐state and transient experiments are performed, where rotor speed and dispersed volume flow rate are changed using the EFCE system toluene–water. OMST deviations are between 3% (droplet sizes in steady state) and 20% (hold‐up in dynamic step‐changes) which are highly dependent on the quality of the parameter estimation.

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Experimental investigation of local bubble properties: Comparison to the sectional quadrature method of moments

et al. 2019

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In recent years, population balance models coupled to computational fluid dynamics have been used as a tool to model bubbly flows. In this work, we established a setup to measure the local size distribution, the velocity and orientation of bubbles in different zones of a bubble column. As a population balance model, we used the sectional quadrature method of moments for the first time in OpenFOAM to simulate the local change in the bubble size distribution and compared its results to the quadrature method of moments as well as to the experimental results. A satisfactory agreement between local experimental values of three investigated flow rates and simulations were found and enables the characterization of heterogeneous bubbly regimes as found in industrial reactive bubble columns.

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The OPOSPM as a Nonlinear Autocorrelation Population Balance Model for Dynamic Simulation of Liquid Extraction Columns

Cited by 18 publications

References 4 publications

Parameter optimisation and validation for droplet population balances

Parameter optimisation and validation for droplet population balances

Online monitoring, simulation and prediction of multiphase flows

Experimental investigation of local bubble properties: Comparison to the sectional quadrature method of moments

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