Naim M. Faqir

LLECMOD: A Bivariate Population Balance Simulation Tool for Liquid- Liquid Extraction Columns

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 equations (for the continuous and discrete phases), experimen- tal correlations are used for the estimation of the turbulent energy dissipation and the slip velocities of the moving droplets along with interaction frequencies of breakage and coalescence. The design of LLECMOD is flexible in such a way that allows the user to define droplet terminal velocity, energy dissipation, axial dispersion, breakage and coalescence frequen- cies and the other internal geometrical details of the column. The user input dialog makes the LLECMOD a user-friendly program that enables the user to select the simulation parameters and functions easily. The program is reinforced by a pa- rameter estimation package for the droplet coalescence models. The scale-up and simulation of agitated extraction col- umns based on the populations balanced model leads to the main application of the simulation tool.

Optimal moving and fixed grids for the solution of discretized population balances in batch and continuous systems: droplet breakage

Abstract The numerical solution of droplet population balance equations (PBEs) by discretization is known to suffer from inherent finite domain errors (FDE). Tow approaches that minimize the total FDE during the solution of discrete droplet PBEs using an approximate optimal moving (for batch) and fixed (for continuous systems) grids are introduced. The optimal grids are found based on the minimization of the total FDE, where analytical expressions are derived for the latter. It is found that the optimal moving grid is very effective for tracking out steeply moving population density with a reasonable number of size intervals. This moving grid exploits all the advantages of its fixed counterpart by preserving any two pre-chosen integral properties of the evolving population. The moving pivot technique of Kumar and Ramkrishna (Chem. Eng. Sci. 51 (1996b) 1333) is extended for unsteady-state continuous flow systems, where it is shown that the equations of the pivots are reduced to that of the batch system for sufficiently fine discretization. It is also shown that for a sufficiently fine grid, the differential equations of the pivots could be decoupled from that of the discrete number density allowing a sequential solution in time. An optimal fixed grid is also developed for continuous systems based on minimizing the time-averaged total FDE. The two grids are tested using several cases, where analytical solutions are available, for batch and continuous droplet breakage in stirred vessels. Significant improvements are achieved in predicting the number densities, zero and first moments of the population.

Optimization of solar pond electrical power generation system

This paper investigates the potential of using a solar pond for the generation of electricity in Jordan. A solar pond power plant model is presented to simulate and optimize such a system under the Jordanian climatic conditions. A Rankine cycle analysis is carried out using an environmentally friendly working fluid, Refrigerant 134a. It was found that using a solar pond for the generation of electricity in Jordan has the potential, with the cost of 0.234 JD/kWh when using a pond of surface area of 1.5 km2, to generate 5 MWe.

Simulation of glucose isomerase reactor: optimum operating temperature

A design equation for immobilized glucose isomerase (IGI) packed bed reactor is developed assuming enzyme deactivation and substrate protection. The developed equation is used to simulate the performance of the reactor at various temperatures (50–80 °C). Enzyme deactivation is significant at high temperature. Substrate protection showed to have significant effect in reducing enzyme deactivation and increasing the enzyme half-life. Factors affecting the optimum operating temperature are discussed. The optimum operating temperature is greatly influenced by the operating period and to a lesser extent with both initial glucose concentration and glucose conversion.Two modes of reactor operation are tested i.e., constant feed flow rate and constant conversion. Reactor operating at constant conversion is more productive than reactor operating at constant flow rate if the working temperature is higher than the optimum temperature. Although at lower temperatures than the optimum, the two modes of operation give the same result.

Drying of an Activated Carbon Column after Steam Regeneration

Experiments of the adsorption cycles, which include adsorption, steam desorption, and drying/cooling, are conducted using a well instrumented pilot-scale apparatus with toluene as the sorptive. Special attention can be paid to the temperature profiles and the changes in water and toluene loading during drying since there is the possibility to take samples from inside the column. Water isotherms were gravimetrically determined and correlated with the association theory of Talu and Meunier. The mathematical description of the air drying of the packed bed with activated carbon is based on an equation system with coupled heat and mass transfer between the bed and the fluid. The first calculations show good agreement with experimental results.

Solution of the population balance equation for liquid-liquid extraction columns using a generalized fixed-pivot and central difference schemes

Abstract In this work, the so-called fixed pivot technique is generalized to discretize the full population balance equation describing the hydrodynamics of liquid-liquid extraction columns (LLEC) with respect to droplet diameter. The spatial variable is discretized in a conservative form using a couple of the recently published central difference schemes. These schemes are combined with an implicit time integration method that is essentially noniterative by lagging the nonlinear terms. The combined numerical algorithm is found fast enough for the purpose of simulating the performance of the LLECs.

The bivariate spatially distributed population balance equation: An accurate reduction technique

Abstract In this work, the advantages of the generalized fixed pivot technique as extended to mass transfer and the quadrature method of moments are utilized to reduce the bivariate spatially distributed population balance equation describing the coupled hydrodynamics and mass transfer in liquid-liquid extraction columns. The proposed reduction technique is found to reduce the discrete system of partial equations from 2M x + 1 to M x + 2 , where M x is the number of pivots or classes. The spatial variable is discretized in a conservative form using a couple of recently published central difference schemes. The numerical predictions of the detailed and reduced models are found almost identical accompanied by a substantial reduction of the CPU time as a characteristic of the reduced model.

Solution of the population balance equation using the sectional quadrature method of moments (SQMOM)

A numerical framework is introduced for solving the population balance equation based on accurately conserving (from theoretical point of view) an unlimited number of moments associated with the particle size distribution. The key idea inthis work is based on the concept of primary and secondary particles, where the former is responsible for the distribution reconstruction while the latter one is responsible for different particle interactions such as breakage and coalescence. The numerical method is found to assemble all the advantages and disadvantages of the sectional and moment methods and hence the name: SQMOM. The method is illustrated here by considering pure breakage in a well-stirred vessels; however, it is already extended and tested for particle coalescence (agglomeration) and growth.

An approximate Optimal Moving Grid technique for the solution of Discretized Population Balances in Batch

Abstract The numerical solution of droplet population balance equations by discretization is known to suffer from inherent finite domain errors (FDE). A new technique that minimizes the total FDE during the solution of discretized population balance equations (DPBE) using an approximate optimal moving grid for batch systems is established. This optimal technique is found very effective for tracking out steeply moving population density with a reasonable number of size intervals. The present technique exploits all the advantages of its fixed counterpart by preserving any two moments of the evolving population. The technique is found to improve the predictions of the number density, zero and first moments of the population.