Use of genetic algorithms and gradient based optimization techniques for calcium phosphate precipitation

Phase equilibrium computations constitute an important problem for designing and optimizing crystallization processes. The Gibbs free energy is generally used as an objective function to find phase amount and composition at equilibrium. In such problems, the Gibbs free energy may be a quite complex function, with several local minima. This paper presents a contribution to handle this kind of problems by implementation of an optimization technique based on the successive use of a genetic algorithm (GA) and of a classical sequential quadratic programming (SQP) method: the GA is used to perform a preliminary search in the solution space for locating the neighborhood of the solution. Then, the SQP method is employed to refine the best solution provided by the GA. The basic operations involved in the design of the GA developed in this study (encoding with binary representation of real values, evaluation function, adaptive plan) are presented. Several test problems are first presented to demonstrate the validity of the approach. Then, calcium phosphate precipitation which is of major interest for P-recovery from wastewater, has been chosen as an illustration of the implemented algorithm

CFD modelling of two-phase stirred bioreaction systems by segregated solution of the Euler–Euler model

An advanced study of a bioreactor system involving a Navier–Stokes based model has been accomplished. The model allows a more realistic impeller induced flow image to be combined with the Monod bioreaction kinetics reported previously. The time-course of gluconic acid production by Aspergillus niger strain is simulated at kinetic conditions proposed in the literature. The simulation is based on (1) a stepwise solution strategy resolving first the fluid flow field, further imposing oxygen mass transfer and bioreaction with subsequent analysis of flow interactions, and (2) a segregated solution of the model replacing the multiple iterations per grid cell with single iterations. The numerical results are compared with experimental data for the bioreaction dynamics and show satisfactory agreement. The model is used for assessment of the viscosity effect upon the bioreactor performance. A 10-fold viscosity rise results in 2-fold decrease of KLa and 25% decrease of the specific gluconic acid production rate. The model allows better understanding of the mechanism of the important bioprocess

Gas maldistribution in a fermenter stirred with multiple turbines

The study is focused on modeling of gas maldistribution of aerated liquid systems in a multiple impeller bioreactor. The phenomenon may or may not depend on column design. The latter case is dependent merely on bed fluid dynamics and could be treated by using the methodology of the residence time distribution (RTD) theory. Accordingly, a specific methodology is proposed, as follows: the fermenter has been modelled as a reactor network involving a combination of zones representing basic ideal flow patterns. The methodology is based on the wide-spread experimental gas tracer technique extended by a new systemic identification approach. The approach is based on a Mellinmodification of the Laplace transform over the relevant equations. The method allows zero-time solutions for identification analysis. Unlike the diffusion model approximation, the technique considered allows exact approximation of the RTD curves with circulation. The proposed transfer function represents adequately the bioreactor gas maldistribution thus allowing fast overview of the studied reaction and prompt feed back control on the physical situation

Calcium phosphate precipitation modeling in a pellet reactor

The calcium phosphate precipitation in a pellet reactor can be evaluated by two main parameters: the phosphate conversion ratio and the phosphate removal efficiency. The conversion ratio depends mainly on the pH. The pellet reactor efficiency depends not only on pH but also on the hydrodynamical conditions. An efficiency model based on a thermochemical precipitation approach and an orthokinetic aggregation model is presented. In this paper, the results show that optimal conditions for pellet reactor efficiency can be obtained

Minimizing water and energy consumptions in water and heat exchange networks.

This study presents a mathematical programming formulation for the design of water and heat exchangers networks based on a two-step methodology. First, an MILP (mixed integer linear programming) procedure is used to solve the water and energy allocation problem regarding several objectives. The first step of the design method involves four criteria to be taken into account., ie, fresh water consumption (F1), energy consumption (F2), interconnection number (F3) and number of heat exchangers (F4). The multiobjective optimization Min [F1, F2] is solved by the so-called ɛ-constraint method and leads to several Pareto fronts for fixed numbers of connections and heat exchangers. The second step consists in improving the best results of the first phase with energy integration into the water network. This stage is solved by an MINLP procedure in order to minimize an objective cost function. Two examples reported in the dedicated literature serve as test bench cases to apply the proposed two-step approach. The results show that the simultaneous consideration of the abovementioned objectives is more realistic than the only minimization of fresh water consumption. Indeed, the optimal network does not necessarily correspond to the structure that reaches the fresh water target. For a real paper mill plant, energy consumption decreases of almost 20% as compared with previous studies

On the flexibility of an eco-industrial park (EIP) for managing industrial water

In a recent paper, a generic model, based on a multiobjective optimization procedure, for water supply system for a single company and for an eco-industrial park was proposed and illustrated by a park involving three companies A, B and C. The best configuration was identified by simultaneously minimizing the fresh water flow rate, the regenerated water flow rate and the number of connections in the eco-industrial park. The question is now to know what the maximal increase/decrease in pollutant flow rates is, so that the eco-industrial park remains feasible, economically profitable and environmentally friendly. A preliminary study shows that the park can accept an increase of pollutant flow rates of 29% in company A, 12% in company B and only 1% in company C; beyond these limits the industrial symbiosis becomes not feasible. The proposed configuration is not flexible with a very limited number of connections. Indeed, the solution implemented for conferring some flexibility to this network is to increase the number of connections within the park. However, connections have a cost, so the increase of their number needs to remain moderate. The number of connections is augmented until the symbiosis becomes unfeasible, or until the gain for each company to participate to the park becomes lower than a given threshold. Several cases are studied by increasing the pollutant flow rates under two different scenarios: 1) in only one company, 2) in two or three companies simultaneously

A multiobjective optimization framework for multicontaminant industrial water network design.

The optimal design of multicontaminant industrial water networks according to several objectives is carried out in this paper. The general formulation of the water allocation problem (WAP) is given as a set of nonlinear equations with binary variables representing the presence of interconnections in the network. For optimization purposes, three antagonist objectives are considered: F1, the freshwater flow-rate at the network entrance, F2, the water flow-rate at inlet of regeneration units, and F3, the number of interconnections in the network. The multiobjective problem is solved via a lexicographic strategy, where a mixed-integer nonlinear programming (MINLP) procedure is used at each step. The approach is illustrated by a numerical example taken from the literature involving five processes, one regeneration unit and three contaminants. The set of potential network solutions is provided in the form of a Pareto front. Finally, the strategy for choosing the best network solution among those given by Pareto fronts is presented. This Multiple Criteria Decision Making (MCDM) problem is tackled by means of two approaches: a classical TOPSIS analysis is first implemented and then an innovative strategy based on the global equivalent cost (GEC) in freshwater that turns out to be more efficient for choosing a good network according to a practical point of view

A thermochemical approach for calcium phosphate precipitation modeling in a pellet reactor

A common pathway for P-recovery from wastewater is phosphate precipitation as calcium phosphates. In this paper, a thermodynamic model for phosphate precipitation is proposed based on various models of activity coefficients taking into account various calcium phosphate phases which can crystallize in the range of pH to be considered, i.e. both dicalcium phosphate dihydrate (DCPD) and amorphous calcium phosphate (ACP) for pH lower than 7.3 and only ACP for pH higher than 7.3. The parameters include the solubility products of ACP and DCPD species. The observed discrepancy in liquid phase equilibrium constants reported in the literature leads to determination of an uncertainty zone describing the precipitation domain. The results obtained offer interesting possibilities for a further optimization of process operating conditions, i.e. determining Ca/P molar ratio, in order to reduce effluent pH (thus avoiding post-treatment) and, consequently, to maximize reactor efficiency

Modeling of residence time distribution : application to a three-phase inverse fluidized bed based on a Mellin transform

The study is focused on modeling of gas and liquid residence time distribution in an aerated liquid system of an inverse fluidized bed bioreactor. Two opposite strategies are currently available: the use of powerful complex computational fluid dynamics (CFD) simulation and the phenomenological semi-empirical models. In this work, a specific methodology is proposed, as follows: the reactor is modeled as a reactor network containing a combination of zones with basic ideal flow patterns such as perfect mixed flow (PMF) and plug flow (PF). The approach is based on a Mellin-modification of the Laplace transformation over the relevant equations. The method allows zero-time solutions for identification analysis. The study shows that the increase of the gas flowrate leads to higher mixing intensity of the gas phase. Decreasing the gas velocity, the inverse fluidized bed tends to perform as a plug flow reactor. The liquid phase performs closer to disperse plug flow

Liquid membrane extraction of bio-active amphiphilic substances: Recovery of surfactin

The interest of application of liquid membrane (pertraction) processes for recovery of biosurfactants from aqueous media was demonstrated. Transport of pure surfactin in three-liquid-phase system was studied. Surfactin was successfully extracted from slightly acid media (pH 5.65–6.05) applying batch pertraction in a rotating discs contactor and using n-heptane as liquid membrane. The process efficiencywas found to be strongly affected by the feed solution acidity (83% at pHF 6.05 and 97% at pHF 5.65 after 4 h pertraction). An atypical pH effect was observed when the behaviour of surfactin extraction from aqueous media by non-polar solvents (n-heptane and n-octane)was studied. The obtained high extraction degrees fromboth acid and basic media and the clearly reduced degree of extraction from neutral media could be attributed to the different conformations of surfactin in these media