In this study, low cost biosorbent ̶inactive biomass (IB) granules (dp=0.433mm) taken from drying beds of Al-Rustomia Wastewater Treatment Plant, Baghdad-Iraq were used for investigating the optimum conditions of Pb(II), Cu(II), and Ni(II) biosorption from aqueous solutions. Various physico-chemical parameters such as initial metal ion concentration (50 to 200 mg/l), equilibrium time (0-180 min), pH (2-9), agitation speed (50-200 rpm), particles size (0.433 mm), and adsorbent dosage (0.05-1 g/100 ml) were studied. Six mathematical models describing the biosorption equilibrium and isotherm constants were tested to find the maximum uptake capacities: Langmuir, Freundlich, Redlich–Peterson, Sips, Khan, and Toth models. The best fit to the Pb(II) and Ni(II) biosorption results was obtained by Langmuir model with maximum uptake capacities of 52.76 and 36.97 mg/g for these two ions respectively. While for Cu(II) the corresponding value was 38.07 mg/g obtained with Khan model. The kinetic study demonstrated that the optimum agitation speed was 400 rpm, at which the best removal efficiency and/or minimum surface mass transfer resistance (MSMTR) was achieved. A pseudosecond-order rate kinetic model gave the best fit to the experimental data (R 2 = 0.99), resulting in mass transfer coefficient values of 42.84×10−5, 1.57×10−5 , and 2.85×10−5 m/s for Pb(II), Cu(II), and Ni(II) respectively. The thermodynamic study showed that the biosorption process was spontaneous and exothermic in nature.
In this paper, estimation of system reliability of the multi-components in stress-strength model R(s,k) is considered, when the stress and strength are independent random variables and follows the Exponentiated Weibull Distribution (EWD) with known first shape parameter θ and, the second shape parameter α is unknown using different estimation methods. Comparisons among the proposed estimators through Monte Carlo simulation technique were made depend on mean squared error (MSE) criteria