To navigate through the Ribbon, use standard browser navigation keys. To skip between groups, use Ctrl+LEFT or Ctrl+RIGHT. To jump to the first Ribbon tab use Ctrl+[. To jump to the last selected command use Ctrl+]. To activate a command, use Enter.

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.

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.

In
this work, the Sectional Quadrature Method Of Moments (SQMOM) is
extended to a one-dimensional physical spatial domain and resolved using
the finite volume method. To close the mathematical model, the required
quadrature nodes and weights are calculated using the analytical
solution based on the Two Unequal Weights Quadrature (TUEWQ) 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). Chemical Engineering Science, 64, 742–752). By applying the finite volume method to the spatial domain, we end up with a semi-discreet ordinary differential
equation system which is solved using the MATLAB standard ODE solvers
(ode45). As a case study, the SQMOM is used to investigate the dynamic
behavior of a Kühni DN150 liquid–liquid extraction column. As an
independent validation step, the SQMOM prediction is compared with the
PPBLab software which utilizes the extended fixed pivot technique as a
built-in population balance model solver. Furthermore, the SQMOM is
validated using the available dynamic experimental data from a Kühni
liquid extraction column using water-acetone-toluene chemical test
system. The dynamic analyses of the Kühni column show very interesting
features concerning the coupled column hydrodynamics and mass transfer
and the droplet breakage and coalescence as well.

This
paper shows that one-dimensional (1-D) [and three-dimensional (3-D)
computational fluid dynamics (CFD)] simulations can replace the
state-of-the-art usage of pseudo-homogeneous dispersion or back mixing
models. This is based on standardized lab-scale cell experiments for the
determination of droplet rise, breakage, coalescence and mass transfer
parameters in addition to a limited number of additional mini-plant
experiments with original fluids. Alternatively, the hydrodynamic
parameters can also be derived using more sophisticated 3-D CFD
simulations. Computational 1-D modeling served as a basis to replace
pilot-plant experiments in any column geometry. The combination of 3-D
CFD simulations with droplet population balance models (DPBM) increased
the accuracy of the hydrodynamic simulations and gave information about
the local droplet size. The high computational costs can be reduced by
open source CFD codes when using a flexible mesh generation. First
combined simulations using a three way coupled CFD/DPBM/mass-transfer
solver pave the way for a safer design of industrial-sized columns,
where no correlations are available.

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 thek–εmodel and the local resolution of continuous phase back mixing.

Cognitive radio networks (CRNs) open up the underutilized parts of the licensed spectrum for secondary reuse, so long as this secondary access does not cause harmful interference to the licensed users. Being able to run CRNs in a completely decentralized manner, as opposed to centralized operation, can be quite advantageous, because it avoids the complexity and single point-of-failure issues that arise from the presence of a central controller, and also eliminates the difficult step of establishing and maintaining a common control channel, which can suffer from saturation and malicious attacks. To that end, we propose in this paper a novel decentralized spectrum allocation technique for CRNs that not only provides great performance in terms of high throughput, excellent fairness, and minimal interference between cognitive users but also provides very stable network operation, in which cognitive users do not have to switch their operating frequency quite regularly. This is achieved by systematically observing the history of the spectrum usage to determine the proper channel assignment in the CRN. Our proposed technique is intuitive, is completely decentralized, and allows for quick reaction to changes in the CRN, such as when the primary users licensed to use the spectrum are suddenly activated.

Peer-to-Peer (P2P) networks face the challenge of frequent pollution attacks. In such attacks, malicious peers pollute the network by sharing mislabeled, corrupt or infected content in an attempt to disrupt the system and waste network resources. When faced by such phenomenon, regular peers get discouraged from participating in the P2P network as they find less value in the system. In this work, we investigate the amount of resources required to restrain pollution attacks by means of content validation. We introduce multiple adaptive techniques that can minimize the spread of polluted content, while at the same time reduce the cost of content validation for peers participating in the network. Furthermore, the proposed pollution-restraint techniques are resistant to collusion from malicious peers, and they do not contribute to excessive communication overhead in the P2P network.

The fusion of Wireless Sensor Networks (WSNs) and Cognitive Radio Networks (CRNs) into Cognitive Radio Sensor Networks (CRSNs) is quite an attractive proposal, because it allows a distributed set of low-powered sensor nodes to opportunistically access spectrum bands that are underutilized by their licensed owners (called primary users (PUs)). In addition, when the PUs are actively transmitting in their own bands, sensor nodes can switch to energy harvesting mode to obtain their energy needs (for free), to achieve almost perpetual life. In this work, we present a novel and fully distributed MAC protocol, called S-LEARN, that allows sensor nodes in a CRSN to entwine their RF energy harvesting and data transmission activities, while intelligently addressing the issue of disproportionate difference between the high power necessary for the node to transmit data packets and the small amount of power it can harvest wirelessly from the environment. The presented MAC protocol can improve both the network throughput and total harvested energy, while being robust to changes in the network configuration. Moreover, S-LEAR

Cognitive radio is an emerging wireless technology that is envisaged as a solution to the spectrum scarcity issue. To improve spectrum utilization, cognitive (unlicensed) wireless users are assigned an opportunistic access to vacant channels on the condition they avoid interference with primary (licensed) users. In this paper we present an impressive design of a low complexity and high efficiency dynamic spectrum access technique for cognitive radio networks. This spectrum assignment algorithm does not require central controllers nor the pre-establishment and maintenance of common control channels. Yet, it can provide throughput and fairness levels that approach the performance of centralized systems. In addition, the proposed technique reacts extremely well to disturbances in the cognitive radio network configuration, including when primary users are activated, or when newcomer cognitive users join the network. Furthermore, we present in this work an analytical model that can be used to provide quick predictions of the performance of our proposed algorithm.

A steady-state one-dimensional heat transfer method was used to measure the effective thermal conductivity of Sultani and El-Lajjun oil shale particles. The particles were packed in a cylindrical bed and heated uniformly over a temperature range of 25 to 250°C. The effect of particle sizes of < 250, 500-710, and 1000-1400 w m on thermal conductivity was also investigated. The effective thermal conductivity of the samples was observed to decrease with increasing temperature. Moreover, the values of thermal conductivity were found to increase with increasing oil content of the shale samples. Over the tested range, particle size showed little effect on thermal conductivity

In this investigation, spectroscopic (FT-IR, UV–Vis, 1H NMR) and chromatographic (GC) techniques were used to analyze two Jordanian shale oils, Sultani and El-Lajjun. The oils were extracted at different pyrolysis temperatures (400–500 °C) using a fluidized bed reactor. The spectroscopic and chromatographic analyses show that the variation of pyrolysis temperature has no significant effect on the composition of the produced oil. The 1H NMR results indicate that the protons of methyl and methelyene represent the bulk of the hydrogen (∼90%) in most shale oil samples. GC analysis reveals that the oil samples contain n-alkanes with a predominant proportion of n-C25.

Batch
charges of Jordanian oil shales were burnt in a laboratory scale
fluidized bed of sand. The effect of shale particle size, initial bed
temperature, superficial gas velocity, sand size, and batch weight on
the burnout time was investigated. Visual observation of shale burnout
time, on-line CO2 concentrations in flue gas and bed temperature
variation were measured simultaneously during the combustion process.
The results have shown, in general, that an increase in bed temperature
or superficial gas velocity was associated with a decrease in burnout
time. On the contrary, an increase in particle mean size led to an
increase in burnout time. The burnout time was analyzed based on the
shrinking-core model, and the results indicated that chemical kinetics,
rather than diffusion, significantly influenced the combustion process.

In
this work, supercritical extraction of Jordanian oil shale was
investigated experimentally using a batch autoclave device. Operating
conditions such as solvent type, mixing time, temperature, pressure, and
particle size effects on oil recovery from oil shale have been studied.
The results indicated that oil yield increases with the increase of
pressure and temperature. The maximum extract yields of 15 and 16 wt%
were obtained at 42 bars and 318°C with toluene for El-Lajjun and
Sultani shales, respectively. Supercritical fluid extraction (SFE) has
shown to be an efficient technique since the extracted yield was 55%
more than the yield obtained using the classical Fischer Assay retorting
process.

In this work, combined thermal decomposition and extraction of Jordanian oil shale was investigated experimentally using a batch autoclave device and toluene as a solvent. The results indicated that oil yield increases with the increase of temperature and extracting time. The maximum extract yields of 16%, 9.5% and 6% by weight were obtained at 42 bars and 318°C, 200°C and 150°C, respectively. Supercritical condition of toluene (42 bars, 318°C) has shown to be a significant one since the extracted yield was 55% more than that obtained by a classical Fischer Assay experiment. Kinetic analysis based on film theory has indicated that the rate of extraction was controlled by the diffusion of extract.