Optimization of a Treatment System of Wastewater Streams for Electrochemical Cr(VI) Reduction: Selective versus Centralized Treatment
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,
Abstract
The problem of the optimization of selective treatment systems of wastewater streams contaminated with hexavalent chromium [Cr(VI)] is investigated. In order to comply with the Mexican environmental norm of Cr(VI) for treated wastewater streams at minimum cost, a nonlinear programming (NLP) model for the electrochemical reduction of hexavalent chromium to trivalent chromium was developed. The model incorporates a variable reaction rate, which is a function of the Cr(VI) concentration and the electrical current density of the electrochemical process. For this purpose, a basic superstructure of the effluent treatment is proposed. The superstructure is composed of three continuous electrochemical reactors without recirculation, and it may produce either a series and/or parallel design topology. The NLP model was used to minimize the objective function, defined as the total annual cost (TAC), which includes the capital cost of each electrochemical reactor, the electrical energy cost and the cost of the treatment of the wastewater streams. In order to investigate the solution set of the proposed NLP model, i. e., to improve the possibilities of obtaining optimum solutions based on economic criteria, a multi-start algorithm was implemented. Two example problems are used to show the versatility of the model and different local optimal solutions were obtained for each case study. The results show that a selective treatment of wastewater streams based on the search of local optimal solutions yields significant savings with respect to a centralized treatment design.
Acknowledgements
ALY would like to acknowledge the support of UAM, México, for the academic scholarship and the financial support of this graduate project.
Nomenclature
- Abbreviation
- NLP
nonlinear programming
- TAC
total annual cost
- Cr(III)
trivalent chromium
- Cr(VI):
hexavalent chromium
- Symbols
- M1
mixer 1
- M2
mixer 2
- M3
mixer 3
- M4
mixer 4
- Uk
treatment units
- Indices
- i
index for wastewater streams
- k
index for unit treatment
- l
index for streams that go from one treatment unit to another
- e
index of discharge point
- L
index of lower bound of a decision variable
- U
index of upper bound of a decision variable
- Sets
- I
set of wastewater streams in the basic superstructure.
- K
set of treatment units in the basic superstructure.
- Parameters
- S:
wastewater flow rate, L·min−1
- Ci
concentration of pollutant in each wastewater stream, mg·L−1
- ceU
discharge limit for the contaminant Cr(VI) in examples 1 and 2, 0.5 mg·L−1
- cinL
lower limit for inlet concentration in each treatment unit, mg·L−1
- cref
reference concentration for the volumetric cost factor, mg·L−1
- cref
500 mg·L−1
- UF
annual usage factor of the electric consumption of each Uk, UF=0.7, dimensionless
- mU
upper limit for mass load, g min−1
- VL
lower limit for volume, 500 L
- VU
upper limit for volume, 800 L
- IL
lower limit for current density, 0 A·m−2
- IU
upper limit for current density, 500 A·m−2
- Fe
total flowrate in discharge point, L min−1
- T
amortization period for each reactor, 20 years
constant in Table 2 to determine reactor capital cost, 14,000 dimensionless
constant in Table 2 to determine reactor capital cost, 15,400 dimensionless
constant in Table 2 to determine reactor capital cost, dimensionless
material factor for 304 stainless steel, dimensionless
slope of the line in Equation 8, 2.1895 A·V−1
Intercept in Equation 8, 6.6305 A
- Ar
Cathode surface, 0.36 m2
- Positive continuous variables
- fik
segregated flowrate for process stream to treatment unit, L·min−1
- f ki,e
segregated flowrate discharge into the environment, L·min−1
- fi,ak
untreated stream before discharge point, L·min−1
- tk
treatment flow rate through the treatment unit, L·min−1
- tlk
flowrate between treatment units, L·min−1
- tkl,e
flowrate from processing unit to the discharge, L·min−1
- cink
input concentration of the pollutant in each treatment unit, mg·L−1
- coutk
output concentration of the pollutant in each treatment unit, mg·L−1
- coutl
output concentration of the pollutant from one treatment unit to another, mg·L−1
- Δmk
mass flowrate load for the toxic compound in each treatment unit, g·min−1
- cke
pollutant concentration obtained in discharge point, mg·L−1
- Rk
variable removal ratio in each wastewater treatment unit
- Ik
current density in each wastewater treatment unit, A·m−2
- Ek
applied potential in each wastewater treatment unit, V
- CEk
cost in dollars per year of the electric energy for each reactor, US $·year−1
- CFk
unit cost used in Eq. for estimating the cost of treatment of flow, US $·year−1
Cost of equipment in stainless steel 304, US $·year−1
- Vk
reactor volume in each treatment unit, L
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- Modelling Laboratory Fischer-Tropsch Synthesis Using Cobalt Catalysts
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- Optimization of a Treatment System of Wastewater Streams for Electrochemical Cr(VI) Reduction: Selective versus Centralized Treatment
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Articles in the same Issue
- Preface to the Special Issue Dedicated to the International Energy Conference, IEC 2017: Energy and its Development in the Twenty-First Century: A globalized vision
- Modelling Laboratory Fischer-Tropsch Synthesis Using Cobalt Catalysts
- Experimental and Kinetic Production of Ethanol Using Mucilage Juice Residues from Cocoa Processing
- Optimization of a Treatment System of Wastewater Streams for Electrochemical Cr(VI) Reduction: Selective versus Centralized Treatment
- Fractal Analysis of pH Time-Series of an Anaerobic Digester for Cheese Whey Treatment
- Optimization of Biomass-to-Bioenergy Logistics Network Design Problem: A Case Study
- Biodiesel production using immobilized lipase supported on a zirconium-pillared clay. Effect of the immobilization method
- Evaluation of Inlet Design and Flow Rate Effect on Current Density Distribution in a Microbial Electrolysis Cell Using Computational Simulation Techniques, Coupling Hydrodynamics and Bioanode Kinetics.
- Nitrogen Adsorption Compounds in the Presence of Dibenzothiophene on Mesoporous Materials for Obtaining Ultra-Low-Sulfur Diesel
- Effect of Mg as Impurity on the Structure of Mesoporous γ-Al203: Efficiency as Catalytic Support in HDS of DBT
- The Effect of Turbulence on Momentum and Heat Transport in Packed Beds with Low Tube to Particle Diameter Ratio
