Granulated Activated Carbon Filter Model & Simulations

Razvan Carbunescu Sarah JohnstonMona Crump Brett McCullough

Daniel Guidry

What is GAC?

GAC stands for Granular Activated Carbon

It is a low volume, high surface area material

The carbon based material is converted to activated carbon by thermal decomposition in a furnace using a controlled atmosphere and heat.

GAC Filter Description The Glass beads

and wool evenly disperse air flow.

A syringe pump empties pollutants into the air supply.

GAC Properties – Adsorption

The pores in activated carbon result in a large surface area.

A gram of activated carbon can have a surface area of 500 to 1500 meters squared.

One pound of GAC, about a quart in volume, can have a total surface area of 125 acres

Biofilter Considerations

• Biofilters are sensitive to Input loading.

• Too much or too little load can disrupt the effectiveness of the biofilter.

• GAC filters can help to alleviate drastic oscillations in biofilter input loading by providing a steady load.

0ppm (no load) factory output

GAC releases stored contaminant

500ppm GAC output / Biofilter input

Providing a Steady State Inputto the Biofilter

For Example:

500ppm typical median factory output

GAC passes load through at same level

500ppm GAC output / Biofilter input

1000ppm “shock loading” factory output

GAC reduces excess load to biofilter

500ppm GAC output / Biofilter input

Equations – Mobile Phase

Equations – Pore Phase

Equations – Non-linear equation

1.3 The non-linear coupling equation

Matrix Approximations

We use MATLAB to calculate the matrices needed to approximate the functions

More Legendre roots means a better approximation for the derivatives and a better approximation for the general functions

Legendre Roots are given from the tables by Stroud and Secrest(1966) up to thirty significant digits

Matrix Approximations

Radial – symmetric, spherical geometry Used to approximate the carbon beads

themselves

W= ( 0.09491 0.19081 0.04762 )

W = ( 0.0098 0.0349 0.0635 0.0819 0.0796 0.0541 0.0095 )

-62.623 80.052 -25.737 13.188 -7.9903 4.9756 -1.8647 22.579 -82.222 75.799 -23.892 12.242 -7.1015 2.5966 -3.984 41.6 -109.32 90.627 -27.8 13.572 -4.6954 1.5827 -10.166 70.264 -166.99 132.72 -39.386 11.975 -0.98636 5.3578 -22.169 136.52 -322.49 255.95 -52.178 0.90471 -4.578 15.942 -59.671 377.01 -1024.3 694.74 46.257 -195.81 488.51 -1024.6 2044.8 -3127.2 1768

-15.66996 20.03488 -4.36492 9.96512 -44.33004 34.36492 26.93285 -86.9329 60.00000

B = ( )

B = ( )

Matrix Approximations

Axial – non-symmetric, planar geometry Used to approximate the flow itself

-3 4 -1-1 0 1 1 -4 3

A =

A =

( )

( ) -43.0014 47.9927 -6.6848 2.6155 -1.6079 1.3628 -1.6765 0.9997 -18.2773 14.2907 5.1519 -1.7720 1.0498 -0.8770 1.0728 -0.6389 5.2138 -10.5516 2.3498 4.1637 -1.9552 1.5125 -1.7966 1.0636 -2.6370 4.6889 -5.3795 0.5063 4.1903 -2.5266 2.7791 -1.6215 1.6212 -2.7784 2.5267 -4.1912 -0.5051 5.3799 -4.6911 2.6381 -1.0631 1.7956 -1.5120 1.9549 -4.1617 -2.3548 10.5570 -5.2158 0.6385 -1.0720 0.8766 -1.0495 1.7711 -5.1525 -14.2884 18.2761 -0.9997 1.6765 -1.3628 1.6079 -2.6155 6.6848 -47.9927 43.0014

Legendre Roots

Axial roots for non-symetric planar geometry now calculated

Radial roots not necessary for calculations

Matlab program solves for the roots of the equations after polynomial is formed

Limited to 80 roots for non-symmetric and 40 roots for symmetric because of the size of the polynomial coeficients

New GAC Filter Interface

Based on the old interface combined with the matlab program

Integrates the resulting graph into the interfcace

Allows for modification of the discretization accuracy

Has initial parameters set

New GAC Filter Interface (cont)

Allows for the specification if the input concentration from an external excel file

Allows for specification of the type of input concentration (steady, intermitent, …)

Allows for the results of the simulation to be saved to an excel file for later use

Allows for adding an experimental data set to the graph to compare results

New GAC Filter Interface (cont)

3 Axial Points 3 Radial Points

0 50 100 150 200 250-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4Solution for 1 Component Charge phase

Time in hours

C/C

0

0 20 40 60 80 100 120 140 160 180-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4Solution for 1 Component Charge phase

Time in hours

C/C

0

Comparison of experimental results versus simulation results with 3 axial points and 3 radial points

5 Axial Points 3 Radial Points

0 20 40 60 80 100 120 140 160 1800

0.2

0.4

0.6

0.8

1

1.2

1.4Solution for 1 Component Charge phase

Time in hours

C/C

0

0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

1.2

1.4Solution for 1 Component Charge phase

Time in hours

C/C

0

Comparison of experimental results versus simulation results with 5 axial points and 3 radial points

7 Axial Points 3 Radial Points

0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

1.2

1.4Solution for 1 Component Charge phase

Time in hours

C/C

0

0 20 40 60 80 100 120 140 160 1800

0.2

0.4

0.6

0.8

1

1.2

1.4Solution for 1 Component Charge phase

Time in hours

C/C

0

Comparison of experimental results versus simulation results with 7 axial points and 3 radial points

Intermittent vs. Continuous Loading

Questions?