## Using the Excel Spreadsheet or the Matlab Files to Calculate Membrane Properties

This page provides general instructions on using the Excel spreadsheet and the Matlab files to calculate membrane parameters with the characterization protocol described in our paper:

Tiraferri, A., Yip, N.Y., Straub, A.P., Romero-Vargas Castrillon, S., and Elimelech,
M. "A Method for the Simultaneous Determination of Transport and Structural
Parameters of Forward Osmosis Membranes", *Journal of Membrane Science*,
Volume 444, October 2013, pages 523–538.
DOI: 10.1016/j.memsci.2013.05.023
PDF File.

Download the Excel File or the Matlab Files (zipped) gratis, for non-commercial use.

#### Instructions for using the Excel spreadsheet

- Solver add-in needs to be enabled in Excel for the spreadsheet to function. Information on enabling the Solver add-in can be found here.
- Enable Macros after opening the spreadsheet.
- In the User Inputs area, enter the bulk NaCl concentration of the draw and feed
solution, in mM, and the corresponding water flux (in L m
^{-2}h^{-1}) and reverse draw salt flux (in milli-moles m^{-2}h^{-1}) for the 1st stage of the experiment. - Repeat step 3 for each of the other three stages (ii, iii, and iv).
- Enter your initial best guess of the membrane water permeability,
*A*, NaCl salt permeability,*B*, and support layer structural parameter,*S*. Having estimates close to the values can help the algorithm find the solution faster. This step is optional and may be skipped. - Click on the "Solve" button. The algorithm will perform a
least-squares non-linear regression, using
*A*,*B*, and*S*as the regression parameters. This may take tens of seconds to a few minutes. - The calculated parameters are displayed in the Results area, along with the
coefficients of determination for water and salt flux,
*R*^{2}. The predicted water and salt fluxes, calculated using the determined membrane parameters, are shown in the results table with the corresponding deviation from the measured experimental values. - To clear the calculations, click on the "Reset" button in the Bounds and Constant area. The spreadsheet will be cleared and ready for another set of calculations.

The spreadsheet calculates bulk osmotic pressures of the draw and feed solution,
*π*, using the van't Hoff equation, and the ratio of the water flux to
reverse salt flux, *J*_{w}/*J*_{s}.

To achieve reasonable confidence in the accuracy of the determined membrane
parameters, it is recommended that the coefficient of variation of the water to
salt flux ratio (CV) be within 10% and that both *R*^{2} values
be higher than 0.95. When reporting the calculated parameters, the values of: (i)
the number of stages employed in the experiment, (ii) the observed CV between
the *J*_{w}/*J*_{s} ratios measured in the various
stages, and (iii) the coefficients of determination calculated by the non-linear
fitting procedure must also be stated.

*The Bounds and Contants area contains user defined values, experimental parameters and universal constants.

The lower and upper bounds constrain the value of the regression parameters the algorithm accepts for the solution. This ensures that the calculated membrane properties are realistic and not an artifact of the code. The NaCl diffusion coefficient is used to calculate the structural parameter based on the extent of internal concentration polarization in the support layer. The gas constant and the experimental temperature are utilized in the van't Hoff equation to determine the bulk osomtic pressures of the draw and feed solution.

#### Instructions for using the Matlab files

- Start MATLAB and switch to the folder containing the MATLAB files (“C:\Users\” in this illustration).
- Launch the graphical user interface (GUI) by typing “ABS_gui” in the main MATLAB command window. The GUI appears as a separate window.
- Enter the initial estimates for the water and salt permeability, and
structural parameter (default values:
*A*_{o}= 1.0 L m^{-2}h^{-1}bar^{-1},*B*_{o}= 0.1 L m^{-2}h^{-1},*S*_{o}= 700*μ*m). Enter the operating temperature (in K) and draw solute bulk diffusion coefficient (in m^{2}/s). - The experimentally measured fluxes and concentrations
*must*be contained in an Excel file (*.xls or *.xlsx) and organized as shown below: - Load the Excel spreadsheet containing the experimental data by clicking on “Load Data” and selecting the data file to be analyzed. The Excel file needs to be located in the same directory as the MATLAB files.
- Double click on the file icon to initiate the calculation. The membrane transport parameters that result from fitting the experimental data to the forward osmosis transport equations will appear under “Output”; the coefficients of determination of the water and draw solute model equations will appear under “Statistics”.

To achieve reasonable confidence in the accuracy of the determined membrane
parameters, it is recommended that the coefficient of variation of the water to
salt flux ratio (CV) be within 10% and that both *R*^{2} values
be higher than 0.95. When reporting the calculated parameters, the values of:
(i) the number of stages employed in the experiment, (ii) the observed CV between
the *J*_{w}/*J*_{s} ratios measured in the various
stages, and (iii) the coefficients of determination calculated by the non-linear
fitting procedure must also be stated.