Rakesh Govind

Algebraic characteristics of extended fuzzy numbers

Abstract Extended fuzzy numbers, previously called fuzzy intervals, are discussed by using the resolution identity and the extension principle. The regularity and the spread are defined for describing the algebraic properties of extended fuzzy numbers. Arithmetic operations on α-level set intervals are suggested instead of general set operations in order to reduce the amount of computation. A sufficient and necessary condition for solving A + X = C is derived. The exact solution for A + X = C is obtained. Finally, A − A = θ (a fuzzification of the crisp 0), which is a natural extension from the nonfuzzy field, is proved.

Advances in biotreatment of acid mine drainage and biorecovery of metals: 1. Metal precipitation for recovery and recycle.

Acid mine drainage (AMD), an acidic metal-bearingwastewater, poses a severe pollution problem attributedto post mining activities. The metals usuallyencountered in AMD and considered of concern for riskassessment are arsenic, cadmium, iron, lead, manganese,zinc, copper and sulfate. The pollution generated byabandoned mining activities in the area of Butte, Montanahas resulted in the designation of the Silver Bow Creek–ButteArea as the largest Superfund (National Priorities List) sitein the U.S. This paper reports the results of bench-scalestudies conducted to develop a resource recovery basedremediation process for the clean up of the Berkeley Pit.The process utilizes selective, sequential precipitation (SSP)of metals as hydroxides and sulfides, such as copper, zinc,aluminum, iron and manganese, from the Berkeley Pit AMDfor their removal from the water in a form suitable foradditional processing into marketable precipitates and pigments.The metal biorecovery and recycle process is based on completeseparation of the biological sulfate reduction step and themetal precipitation step. Hydrogen sulfide produced in the SRBbioreactor systems is used in the precipitation step to forminsoluble metal sulfides. The average metal recoveries usingthe SSP process were as follows: aluminum (as hydroxide) 99.8%,cadmium (as sulfide) 99.7%, cobalt (as sulfide) 99.1% copper(as sulfide) 99.8%, ferrous iron (sulfide) 97.1%, manganese(as sulfide) 87.4%, nickel (as sulfide) 47.8%, and zinc (as sulfide)100%. The average precipitate purity for metals, copper sulfide,ferric hydroxide, zinc sulfide, aluminum hydroxide and manganesesulfide were: 92.4, 81.5, 97.8, 95.6 , 92.1 and 75.0%, respectively.The final produced water contained only calcium and magnesiumand both sulfate and sulfide concentrations were below usablewater limits. Water quality of this agriculturally usable watermet the EPAs gold standard criterion.

STUDIES ON BIOSORPTION OF ZINC(II) AND COPPER(II) ON DESULFOVIBRIO DESULFURICANS

Abstract The objectives of these studies are to determine the equilibrium concentration and kinetics of metal sorption on sulfate-reducing bacteria (SRB) isolates. Adsorption establishes the net reversible cellular metal uptake and is related to SRB metal toxicity and the effects of environmental factors. Results from biosorption equilibria and kinetics of copper(II) and zinc(II) ions on Desulfovibrio desulfuricans and the effects of adsorption of these metals on SRB are discussed. Adsorption studies were conducted using stationary phase cells with equilibrium uptake at 24 h and pHs in the range of 4–7. Equilibrium adsorption in milligram of metal/g dry cell for copper(II) of 2.03 (pH 4.0) and 16.7 (pH 5.0) and zinc(II) of 6.40 (pH 5.5), 13.8 (pH 6.0), 39.2 (pH 6.2) and 49.6 (pH 6.6) was measured experimentally. Negligible biosorption of copper and zinc was found below pH 4.0, with metal sorption increasing within a limited range of pH mainly due to the neutral and/or deprotonated state of binding ligands on cell walls. Competition of metal ions during biosorption was investigated by conducting sorption experiments with Zn(II) using potassium phosphate buffer (KP) and deionized/distilled water. Zn(II) sorption capacity was lower in KP buffer than deionized water due to competition from potassium ions. Scanning Electron Microscope micrographs indicated that metal biosorption on SRB may be related to the production of extracellular polymeric substance (e.g., polysaccharide).

Treatment of acid mine drainage: I. Equilibrium biosorption of zinc and copper on non-viable activated sludge

Biosorption is potentially attractive technology for treatment of acid mine drainage for separation/recovery of metal ions and mitigation of their toxicity to sulfate reducing bacteria. This study describes the equilibrium biosorption of Zn(II) and Cu(II) by nonviable activated sludge in a packed column adsorber. The Zn(II) uptake capacity of unconditioned sludge (not subjected to processing other than drying) was found to decrease in repeated adsorption–desorption cycles, declining by a factor greater than 20 from cycle 1 to cycle 6. Equilibrium uptake of metals by dried sludge conditioned by exposure to deionized water at a pH corresponding to that of the feed solution showed a strong pH dependence and was modeled using the Langmuir adsorption isotherm. Equilibrium metal uptakes from solutions containing single metal ion were 2.5 mg g(dry biomass)−1 and 3.4 mg g(dry biomass)−1 for Zn(II), and 1.9 mg g(dry biomass)−1 and 5.9 mg g(dry biomass)−1 for Cu(II) at pH 3.0 and 3.8, respectively. Equilibrium uptakes from binary mixtures were 30% lower than single component solution uptakes for both metals, indicating some competition between the two metals. No hysteresis was detected between adsorption and desorption equilibria. Anion concentration and pH measurements indicated that simultaneous sorption of metal cation and sulfate anion was probably occurring at pH 3.0, while proton exchange predominated at pH 3.8. Results of the study point to the usefulness of non-viable activated sludge as a biosorbent for recovery/separation of metal ions from acid mine drainages.

Biodegradation of toluene in a membrane biofilter

A membrane biofilter is used to biodegrade toluene in the gas phase. Active microorganisms are immobilized on the outside of a hollow fiber membrane cartridge and air containing toluene as the contaminant is passed through the membrane fibers. A porous polysulfone membrane containing water in the pore is used through which both toluene and oxygen are diffused to the biofilm attached to the outside surface. High conversion of toluene (84%) is achieved with a 16 second gas-phase residence time, based on total internal volume of the hollow fibers. A mathematical model is then developed to estimate toluene removal efficiencies at higher air flow rates.

Solutions of algebraic equations involving generalized fuzzy numbers

Abstract This paper deals with algebraic equations involving generalized fuzzy numbers with continuous membership functions. The generalized fuzzy number defined in this paper is a general name for fuzzy numbers, fuzzy intervals, crisp numbers, and interval numbers. Three important properties of the generalized fuzzy numbers with continuous membership functions are introduced as the basis for deriving the solvability criterion. The sufficient and necessary condition for solving A ± X = C is derived. The sufficient and necessary condition for solving A × X = C and A ÷ X = C when A and C are nonzero generalized fuzzy numbers is also derived in this paper. Instead of the inverse operation method, which fails for fuzzy sets, inverse operations on the boundary points of α-level set intervals for continuous membership functions are used when the derived criteria of solvability are satisfied. A unique solution rather than a solution set is obtained.

Advances in biotreatment of acid mine drainage and biorecovery of metals: 2. Membrane bioreactor system for sulfate reduction.

Several biotreatmemt techniques for sulfate conversion by the sulfate reducing bacteria (SRB) have been proposed in the past, however few of them have been practically applied to treat sulfate containing acid mine drainage (AMD). This research deals with development of an innovative polypropylene hollow fiber membrane bioreactor system for the treatment of acid mine water from the Berkeley Pit, Butte, MT, using hydrogen consuming SRB biofilms. The advantages of using the membrane bioreactor over the conventional tall liquid phase sparged gas bioreactor systems are: large microporous membrane surface to the liquid phase; formation of hydrogen sulfide outside the membrane, preventing the mixing with the pressurized hydrogen gas inside the membrane; no requirement of gas recycle compressor; membrane surface is suitable for immobilization of active SRB, resulting in the formation of biofilms, thus preventing washout problems associated with suspended culture reactors; and lower operating costs in membrane bioreactors, eliminating gas recompression and gas recycle costs. Information is provided on sulfate reduction rate studies and on biokinetic tests with suspended SRB in anaerobic digester sludge and sediment master culture reactors and with SRB biofilms in bench-scale SRB membrane bioreactors. Biokinetic parameters have been determined using biokinetic models for the master culture and membrane bioreactor systems. Data are presented on the effect of acid mine water sulfate loading at 25, 50, 75 and 100 ml/min in scale-up SRB membrane units, under varied temperatures (25, 35 and 40 °C) to determine and optimize sulfate conversions for an effective AMD biotreatment. Pilot-scale studies have generated data on the effect of flow rates of acid mine water (MGD) and varied inlet sulfate concentrations in the influents on the resultant outlet sulfate concentration in the effluents and on the number of SRB membrane modules needed for the desired sulfate conversion in those systems. The pilot-scale data indicate that the SRB membrane bioreactors systems can be applied toward field-scale biotreatment of AMD and for recovery of high purity metals and an agriculturally usable water.

Treatment of trichloroethylene (TCE) in a membrane biofilter.

This article reports on the biodegradation of trichloroethylene (TCE) in a hollow‐fiber membrane biofilter. Air contaminated with TCE was passed through microporous hollow fibers while an oxygen‐free nutrient solution was recirculated through the shell side of the membrane module. The biomass was attached to the outside surface of the microporous hollow fibers by initially supplying toluene in the gas phase that flows through the fibers. While studies on TCE biodegradation were conducted, there was no toluene present in the gas phase. At 20‐ppmv inlet concentration of TCE and 36‐s gas‐phase residence time, based on total internal volume of the hollow fibers, 30% removal efficiency of TCE was attained. At higher air flow rates or lower gas‐phase residence times, lower removal efficiencies were observed. During TCE degradation, the pH of the liquid phase on the shell side of the membrane module decreased due to release of chloride ions. A mathematical model was developed to describe the synchronous aerobic/anaerobic biodegradation of TCE.

Fate and effects of semivolatile organic pollutants during anaerobic digestion of sludge

Abstract Anaerobic digestion of primary and secondary sludge containing selected semivolatile organic pollutants was investigated. Typical digester operation was simulated with three, complete-mix, bench-scale digesters maintained at 35.5°C with a 30 day solids retention time. Two digesters were fed a primary and secondary sludge mixture produced from wastewater spiked with twenty semivolatile organics from the CERCLA pollutant list. The remaining digester (the control) was fed a similar mixture of sludge, but with no added organics. Operational parameters were monitored to compare the test and control units. All parameters were found to be within the limits of normal operation. Performance was near identical. An isotope dilution GC/MS method was employed for organics analysis of influent and effluent streams for all reactors. Steady-state fates of the organics were determined by mass balance. Twelve of the chemicals appear consistently and at steady state. Degradation was apparent for all components, with at least 10% of each parent compound partially or completely transformed. Sorption onto digester solids was an important removal mechanism. Results of organic analysis for the control digester highlight the effects of metabolic interferences.

Efficacy of commercial products in enhancing oil biodegradation in closed laboratory reactors

SummaryA laboratory screening protocol was designed and conducted to test the efficacy of eight commercial bacterial cultures and two non-bacterial products in enhancing the biodegradation of weathered Alaska North Slope crude oil in closed flasks. Three lines of evidence were used to support the decision to progress to field testing in Prince William Sound: rapid onset and high rate of oxygen uptake, substantial growth of oil degraders, and significant degradation of the aliphatic and aromatic hydrocarbon fractions of the weathered Alaska North Slope crude oil. A product had to enhance biodegradation greater than that achieved with excess mineral nutrients. Experiments were conducted in closed respirometer flasks and shake flasks, using seawater from Prince William Sound and weathered crude oil from a contaminated beach. Analysis of the data resulted in selection of two of the ten products for field testing. Both were bacterial products. Findings suggested that the indigenous Alaskan microorganisms were primarily responsible for the biodegradation in the closed flasks and respirometer vessels.