FAST is very easy to use. No installation is required, just unzip the FAST folder and run the executable. FAST will open in the main window, where all input and preferences can be set. There are no hidden menus, except from the help window, which will open when the help button is clicked. It shows a detailed explanation of FAST's functionality in a mouse-over mode. Just move the mouse cursor over the text or input fields to get specific help information. After starting the calculation using the "Start calculation" button, FAST will show the calculation progress in a separate window. Output will be stored in a separate output .csv file, which will be automatically opened when the calculation is finished.

The following is a summary of the necessary input parameters and preferences to be set to use FAST. This information can also be found in the FAST help window.

## Experiment type

### Column Breakthrough

Use the Column Breakthrough experiment type to simulate the breakthrough curve of a fixed-bed adsorption filter.

### Batch Reactor

Use the Batch Reactor experiment type to determine mass-transfer coefficients from batch reactor tests, e.g. differential column batch reactor (DCBR), completely mixed basket reactor, completely mixed suspension reactor or similar.

## Model selection

### HSDM - Homogeneous Surface Diffusion Model

The mass balance over the filter follows:

Solid-phase mass transfer is modeled as homogeneous surface diffusion with Fick's second law given in radial coordinates:

### LDF - Linear Driving Force Model

The mass balance over the filter follows:

Solid-phase mass transfer is approximated by a linear driving force.

Select **HSDM (fast)** and the calculation will be done with a greater time step which results in faster computation but may reduce accuracy of the model results. The maximum deviation from HSDM is 3%. This option can be useful if the calculation time of the HSDM is to large and the LDF approximation is not valid.

## Operational parameters

### Empty Bed Contact Time EBCT

The empty bed contact time is calculated as the volume of the bed occupied by the adsorbent media including the porosity volume divided by the flow rate.

Only EBCT or adsorbent mass m can be selected as input parameter, not both. If EBCT is selected as input parameter, m will be calculated from EBCT, flow rate, and bed density.

### Mass of adsorbent m

Adsorbent mass can be given as either dry or wet weight. Be consistent in using dry or wet weight values as input parameters. The adsorbent mass m, bed density, particle density, and equilibrium parameters KF and n have to be based on the same water content. Only EBCT or adsorbent mass m can be selected as input parameter, not both. If m is selected as input parameter, EBCT will be calculated from m, flow rate, and bed density.

### Bed Porosity ε_{B}

The filter bed porosity equals the ratio of void to total volume within a filter layer. It can be calculated from the density of the filter bed and the density of the adsorbent particle.

Only bed porosity or bed density can be selected as input parameter, not both. If bed porosity is selected as input parameter, bed density will be calculated from particle density and bed porosity (above equation).

### Bed density ρ_{B}

The bed or bulk density of the adsorbent in the fixed-bed is defined as ratio of adsorbent mass to volume of the filter bed.

Only bed porosity or bed density can be selected as input parameter, not both. If bed density is selected as input parameter, bed porosity will be calculated from particle density and bed porosity (above equation).

### Particle density ρ_{P}

The particle density (density of the adsorbent grain) includes the inner porosity, but excludes void fraction of the bed. Be consistent in using dry or wet weight values as input parameters. The adsorbent mass m, bed density, particle density, and equilibrium parameters KF and n have to be based on the same water content.

### Particle diameter d_{P}

Diameter of the adsorbent grain particle. If the diameter is distributed within a grain size range use the effective grain size (if known) or average values.

### Influent concentration c_{0}

Influent liquid-phase concentration of the adsorbate. FAST can only deal with constant influent concentrations.

### Flow rate Q

Volumetric flow rate to the adsorber. FAST requires a constant value of the flow rate.

### Bed volume BV

Volume occupied by adsorbent media including porosity volume:

Bed volume is not used as input parameter, but calculated for your convenience. It can be used to verify the dimensions of the filter bed.

## Adsorption equilibrium and kinetic parameters

###
Freundlich isotherm coefficients K_{F} and n

The amount of adsorbate adsorbed is a function of the liquid-phase concentration and called adsorption equilibrium isotherm. Different functions can be used to describe the adsorption equilibrium. In FAST, only Freundlich isotherm data can be used. This adsorption isotherm was proposed by Freundlich (1906) as an empirical equation and is widely used to describe the data for heterogeneous adsorbents.

The Freundlich exponent n (Freundlich adsorption capacity parameter) is unitless. Sometimes (especially in North America), also 1/n is used instead.

The unit of K_{F} is composed by the units of m (mass of adsorbent) and c_{0} (influent concentration). If you change the units of m or c_{0} then the value of K_{F} will be adapted to the new unit. The same, if you change the Freundlich exponent n.

To input the Freundlich parameters, first select the unit of m and c_{0} then input n subsequently K_{F}.

### Film diffusion coefficient k_{L}

also called: liquid-phase mass transfer coefficient

The mass transfer rate through the exterior adsorbent surface is assumed to be proportional to the surface area and the difference in concentration of bulk solution and adsorbent surface:

The film diffusion coefficient k_{L} can be estimated from empirical correlations for the Sherwood number, e. g. the correlations of Wilson and Geankoplis (1966) or Gnielinski(1978). Alternatively, k_{L} can be determined by fitting the simulation to experimental data. To do this, use the multi-run feature by clicking on the parameter symbol.

### Surface diffusion coefficient D_{S}

also called: solid-phase mass transfer coefficient

The mass transport in the adsorbent grain is assumed to be homogeneous surface diffusion and modeled by Fick's second law.

The surface diffusion coefficient D_{S} has to be determined by fitting the simulation to experimental data. To do this, use the parameter variation feature by clicking on the parameter symbol.

## Dimensionless parameters

If this checkbox is activated, user input of the dimensionless groups Bi, St, and n is possible. If this checkbox is not activated, these values will be calculated automatically.

The operational, equilibrium and kinetic parameters defining the shape of the breakthrough curve can be transformed into four remaining dimensionless groups, Bi, St, Dg, and n. If the checkbox "Dimensionless Parameters" is activated, the x-axis format is set as dimensionless time t/ts and thus Dg will be obsolete.

### Solute Distribution Parameter Dg

The solute distribution parameter Dg represents the adsorption equilibrium. Dg is the ratio of solute adsorbed onto the adsorbent grain to that in the liquid phase.

Here, q_{0} is the equilibrium solid-phase concentration corresponding to the influent concentration c_{0}.

A higher Dg implies a shift of the adsorption equilibrium towards the solid-phase, which results in a retarded breakthrough.

### Biot number Bi

The dimensionless Biot number represents the ratio of liquid- to solid-phase mass transfer rate.

Here, q_{0} is the equilibrium solid-phase concentration corresponding to the influent concentration c_{0} and r_{p} is the particle radius d_{p}/2.

The shape of the breakthrough curve can be categorized by the value of the Biot number:

### Stanton number St

The modified Stanton number represents the dimensionless liquid-phase mass transfer coefficient. The lower the value of St, the higher is the influence of film diffusion on the shape of the breakthrough curve.

Here, r_{p} is the particle radius d_{p}/2.

### Freundlich exponent n

In dimensionless form, the Freundlich isotherm has only one parameter: n.

Here, Y is the dimensionless solid-phase concentration and X is the dimensionless liquid-phase concentration. K_{F} and the information about the adsorption equilibrium (i.e., about the time of stoichiometric breakthrough) is included in the solute distribution parameter Dg.

## Miscellaneous

### X-axis format

Select the type of x-axis and input the length of the simulation interval (x-axis maximum).

The effluent concentration of the fixed-bed filter can be plotted against three different quantities:

**Operation time**- the normalized effluent concentration is plotted against operation time in seconds, minutes, hours or days. If the option t/ts is selected, c is plotted against the dimensionless time, i.e. the operation time divided by the ideal (stoichiometric) breakthrough time.**Volume treated**- the normalized effluent concentration is plotted against the throughput volume given in L, m^{3}or relative to the volume of the filter bed (bed volume - BV).**Volume treated by mass**- the normalized effluent concentration is plotted against the throughput volume relative to the adsorbent mass and given in L/kg or m^{3}/kg.

### Start Calculation

This button starts the simulation. During simulation, the progress is reported in a status window. When finished, the simulation results are saved in a file (sim_<random number>.csv) and automatically opened in MS Excel (if installed).

### Multi-run

To enable easy variation of input parameters, e.g. for sensitivity analysis or DS determination, the multi-run feature was added. Simply click the symbol of the parameter to be varied and enter the desired values. FAST will perform multiple simulations (one for each value entered). Parameters can only be varied one at a time.

### No Film Diffusion

With this checkbox activated, liquid-phase mass transfer is neglected.

The boundary condition of the intraparticle transport equation can be chosen:

Checkbox activated

The concentration at the particle surface equals the bulk concentration (no film diffusion). Use this option if film diffusion is definitely not the limiting mass transport step and can be safely neglected.Checkbox not activated

At the exterior adsorbent grain surface, the mass transported into the grain equals the mass transported through the stagnant liquid film.

## Literature

Information on FAST and the related problem of simulating fixed-bed adsorbers can be found in:

Sperlich, A.; Schimmelpfennig, S.; Baumgarten, B.; Genz, A.; Amy, G.; Worch, E.; Jekel, M. (2008): Predicting anion breakthrough in granular ferric hydroxide (GFH) adsorption filters. Water Research 42 (8-9), 2073-2082.

http://dx.doi.org/10.1016/j.watres.2007.12.019

More information on the adsorption theory and the models used in FAST can be found in:

Sontheimer, H., Crittenden, J., Summers, R. (1988): Activated Carbon for Water Treatment. DVGW-Forschungsstelle am Engler-Bunte-Institut der Universität Karlsruhe, Karlsruhe.

Weber, W.J. & Smith, E.H. (1987): Simulation and design models for adsorption processes. Environ. Sci. Technol., 21, 1040-1050.

Worch, E. (1991): On The Prediction Of Multicomponent Adsorption In Fixed-Bed-Adsorbers.1. Mathematical-Model. Chemische Technik, 43, 111-113.

Hand, D.W.; Crittenden, J.C.; Thacker, W.E. (1984): Simplified Models for Design of Fixed-Bed Adsorption Systems, Jour. of Env. Eng. 110 (2), 440-456.

Literature cited:

Freundlich, H. (1906): Über die Adsorption in Lösungen. Z. Phys. Chem. 57, 385-470.

Gnielinski, V. (1978): Gleichungen zur Berechnung des Wärme- und Stoffaustausches in durchströmten ruhenden Kugelschüttungen bei mittleren und großen Pecletzahlen. Verfahrenstechnik 12 (6), 363-367.

Wilson, E.J., Geankoplis, C.J. (1966): Liquid mass transfer at very low Reynolds numbers in packed beds. Ind. Eng. Chem. Fund. 5, 126-129.