Reverse Osmosis Simulation

Reverse Osmosis (RO) Membranes


OLI has developed RO membrane simulation technology. This simulation model offers the ability to evaluate a wastewater stream against different vendor membranes and simulate the behavior of the membrane for a particular chemistry. 


A solution diffusion approach

OLI used a solution-diffusion approach to model the transport mechanism inside the membrane. Following this approach, the model calculates the transfer of ions and water through polymeric membranes via a solution diffusion mechanism, because of dissolution of permeates in the membrane materials [1]. 

The water flux through the membrane is a function of the water permeability coefficient, the hydrodynamic pressure difference and osmotic pressure across the membrane. The solute flux through the membrane is a function of the solute permeability constant and the solute concentration gradient across the membrane [2].

Molecular size of the ions strongly affects the transport characteristics of the ions. This is due to the sieving actions of the membranes. However, in a water-based environment, a different number of water molecules surrounds each cation and anion. Thus, the real radius of an ion, that is, the hydrated ion radius, rather than the absolute ionic crystal radius.  

Regardless of membrane type, or the type of experiment, or the membrane configuration, the salt permeabilities are inversely proportional to the hydrated radii of the ions [3].

In the OLI reverse osmosis membrane model, permeability of ions has been correlated with their hydration numbers. 


In general, the typical order of rejection of cations by reverse osmosis membranes follow Fe3+ > Ni2+   Cu2+ > Mg2+ > Ca2+ > Na+ > K+, and PO43- > SO42- > HCO3- > Br- > Cl- > NO3-  F- for anions [4]. The permeability of cations and anions calculated as a function of hydration numbers follow the typical trends. For some organics with same homologous group (i.e., alcohols, phenols, acids), the rejections have been correlated by calculating the topological parameters characterizing molecular structure [5]. For other neutrals, self-diffusivities relative to water have been used to correlate the permeability.

OLI reverse osmosis (RO) membrane block

As part of OLI's commitment to industrial water treatment simulation, OLI has developed a reverse osmosis membrane block within the software OLI Flowsheet: ESP. Other membrane operations such as forward osmosis are being considered for simulation as well. The RO block can study a specific chemistry in combination with one or more vendor-supplied membranes to simulate performance of a given membrane. The software is vendor-independent and can be used to screen different membranes for optimal membrane selection, or for optimizing membrane performance within a flowsheet environment.

For information on a particular membrane, the RO block relies on the data from commercial membrane manufacturers who provide a public product specification sheet (available on the Internet) for each type of membrane. In addition to physical dimensions (i.e., membrane area), the product sheets also report performance of the membrane (i.e., permeate flux, recovery and rejection percentage for NaCl or other solutes) at specific test conditions.


User-entered test conditions data can then be entered for this membrane data.  The user's actual test condition data are the key information for calculating the permeability coefficients of water and the test solute for the membrane element. These calculated permeability coefficients along with the above-mentioned correlations are used to estimate the permeability coefficients of other species present. The advantage of this method is that a reasonable and preferential order of permeabilities for the membrane regardless of membrane type can be correctly estimated.  

In the current OLI membrane development, users can enter number of membrane elements per vessel and total number of vessels in the assembly. Alternatively, users can estimate total number of vessels required (or total membrane area) for a specific recovery. Concentration polarization is approximated using Peclet number and intrinsic enrichments [4]. Flow factor (sometimes referred as fouling factor) is estimated from the water activity reduction unless specified by the users. Users may specify feed side pressure drop per element if available.


There are options for conditioning the feed to a specific pH by choosing a pH acid titrant or base titrant. 


[1] S.M.J. Zaidi, F. Fadhillah, Z. Khan, and A.F. Ismail. Salt and water transport in reverse osmosis thin film composite seawater desalination membranes. Desalination, 368 (2015) 202.

[2] P. Mukherjee, A. Sengupta. Ion exchange selectivity as a surrogate indicator of relative permeability of ions in reverse osmosis processes. Environ. Sci. Technol., 37 (2003) 1432.

[3] S.M.S. Ghiu, Mass transfer of ionic species in direct and reverse osmosis processes, Doctoral dissertation, University of South Florida, 2003.

[4] R.W. Baker, Membrane technology and applications, 2nd Ed., Chichester, England: Wiley, 2004.

[5] A. Ksiązczak, A. Anderko. A chemical approach to the prediction of thermophysical properties of associating compounds. Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1988) 496.