Membrane Separation Processes Federico Milella Rate Controlled Separation - Autumn 2017 Separation Processes Laboratory - Institute of Process Engineering
Agenda Introduction Mass balances over a membrane module Reverse osmosis Pervaporation Gas separation Gas membrane module modeling for binary mixtures Marco Mazzotti 16.01.2018 2
Agenda Introduction Mass balances over a membrane module Reverse osmosis Pervaporation Gas separation Gas membrane module modeling for binary mixtures Marco Mazzotti 16.01.2018 3
Membrane module Feed stream A + B T, p, F, z T = temperature p = total pressure F, R, P = molar flow rates x, z = molar fractions Retentate stream A (+B) T r, p r, R, x r Permeate stream B (+A) T p, p p, P, x p A membrane is a selective barrier that allows the passage of certain components and retain others in the liquid or gas mixture. Different membrane modules are implemented for different applications. A membrane process is often composed of several connected modules. Major design variables: membrane area, membrane material, process layout. Major operation variables: pressure, temperature. Marco Mazzotti 16.01.2018 4
Membrane module Feed stream A + B T, p, F, z T = temperature p = total pressure F, R, P = molar flow rates x, z = molar fractions Retentate stream A (+B) T r, p r, R, x r Permeate stream B (+A) T p, p p, P, x p Marco Mazzotti 16.01.2018 5
Agenda Introduction Mass balances over a membrane module Reverse osmosis Pervaporation Gas separation Gas membrane module modeling for binary mixtures Marco Mazzotti 16.01.2018 6
Material balances Feed stream F, z (n, x) z (n, x) z+dz Retentate stream R, x r J i Permeate stream P, x p y, A Marco Mazzotti 16.01.2018 7
Material balances Total material balance Feed stream F, z y, A (n, x) z J i (n, x) z+dz Retentate stream R, x r Permeate stream P, x p Entire membrane module as control volume F = R + P Component material balance F zi = Rx r,i + Px p,i i = 1,, C 1 C i=1 z i = C i=1 x r,i = C i=1 x p,i = 1 n = total molar flow rate x = molar fractions y = spatial coordinate A = membrane area coordinate J = membrane flux Marco Mazzotti 16.01.2018 8
Material balances Total material balance Feed stream F, z y, A (n, x) z J i (n, x) z+dz Retentate stream R, x r Permeate stream P, x p Differential element as control volume F = R + P Component material balance F zi = Rx r,i + Px p,i i = 1,, C 1 C i=1 z i = C i=1 x r,i = C i=1 Total flux across the membrane x p,i = 1 n = total molar flow rate x = molar fractions y = spatial coordinate A = membrane area coordinate J = membrane flux nx i z+dz C i=1 nx i z+dz = dn = JdA, J i = J Component flux across the membrane (nx i ) z+dz nx i z = d nx i = J i da, i = 1,, C 1 Marco Mazzotti 16.01.2018 9
Membrane flux Feed stream Retentate stream F, z, p f J i A δ R, x r Permeate stream P, x p r y To solve the material balances for the membrane module, a constitutive flux equation must be determined. In general, the flux J i is a function of membrane material and operating variables, i.e. pressures and temperature: J i = Ji(membrane material, driving force) Marco Mazzotti 16.01.2018 10
Membrane flux Feed stream Retentate stream Permeate stream To solve the material balances for the membrane module, a constitutive flux equation must be determined. In general, the flux J i is a function of membrane material and operating variables, i.e. pressures and temperature: J i = Ji(membrane material, driving force) Marco Mazzotti 16.01.2018 11
Membrane flux Feed stream Retentate stream Permeate stream To solve the material balances for the membrane module, a constitutive flux equation must be determined. In general, the flux J i is a function of membrane material and operating variables, i.e. pressures and temperature: J i = Ji(membrane material, driving force) Marco Mazzotti 16.01.2018 12
Membrane transport models Two main categories of membranes and two transport models Porous membrane Pore-flow model Permeants are separated by pressure-driven convective flow Separation achieved due to different permeants size Reasonable description for pore diameter > 10 Å Dense membrane Solution-Diffusion model Permeants dissolve into the membrane and diffuse through the membrane under a concentration potential Separation achieved due to different solubility and diffusion rate Reasonable description for equivalent pore diameter < 5 Å Source: R. W. Baker. Membrane Technology and Applications. 2012 Marco Mazzotti 16.01.2018 13
Membrane flux Feed stream Retentate stream F, z, p f J i A δ R, x r Permeate stream P, x p r y To solve the material balances for the membrane module, a constitutive flux equation must be determined. In general, the flux J i is a function of membrane material and operating variables, i.e. pressures and temperature: J i = Ji(membrane material, driving force) We focus on the following applications, where the flux is determined through the solutiondiffusion theory: Reverse osmosis Pervaporation Gas separation Marco Mazzotti 16.01.2018 14
Agenda Introduction Mass balances over a membrane module Reverse osmosis Pervaporation Gas separation Gas membrane module modeling for binary mixtures Marco Mazzotti 16.01.2018 15
Agenda Introduction Mass balances over a membrane module Reverse osmosis Pervaporation Gas separation Gas membrane module modeling for binary mixtures Marco Mazzotti 16.01.2018 16
Selectivity, α [-] Robeson s plot - CO 2 /N 2 Robeson s plot CO 2 /N 2 Permeability, Q [barrers] Marco Mazzotti 16.01.2018 17
Membrane module modeling Binary mixture F, z, p f p p J i (Q, α) A δ R, y r P, y p r z Assumptions Constant membrane properties Q, α Perfectly mixed retentate and permeate Isothermal process Negligible pressure drop at both membrane sides Co-current flow Marco Mazzotti 16.01.2018 18
Membrane module modeling Binary mixture F, z, p f p p J i (Q, α) A δ R, y r P, y p r z Assumptions Constant membrane properties Q, α Perfectly mixed retentate and permeate Isothermal process Negligible pressure drop at both membrane sides Co-current flow Marco Mazzotti 16.01.2018 19