Week 6 - Exercise

Problem Statement

Continuous slurry adsorption is carried out to reduce the pollutant content in an aqueous stream from an inlet concentration of 1x10\(^{-2}\) mol l\(^{-1}\) . The flowrate of the aqueous stream is 50 m\(^3\) h\(^{-1}\) . The adsorbent flowrate is 750 kg h\(^{-1}\). The residence time is 3 h.

Adsorption is controlled by external mass transfer with a coefficient k\(_L\)= 0.5 m h\(^{-1}\). The adsorbent particles have a surface area of 10 m\(^2\) kg\(^{-1}\) and a density of 1850 kg m\(^{-3}\). Consider a linear isotherm of the form \(q=kc\), where \(q\) [mol kg\(^{-1}\)] is the amount of phenol adsorbed per kg of adsorbent, \(c\) is the molar concentration of pollutant in solution and \(k=1\times{10}^4\) [l kg\(^{-1}\)] is the partition coefficient.

Determine the steady state concentration of pollutant in the aqueous stream leaving the unit.