Ceramic Water Filter with Activated Carbon Core

This example illustrates how to model the transport of different contaminants through a ceramic water filter candle with an activated carbon core. This type of water filter can be found in tabletop gravity filters as well as attached to the faucet or as part of a larger reverse osmosis filter system. It shows how to set up the flow and transport equations to model different filter mechanisms and examines the effect of a small fracture in the ceramics part.

Our drinking water contains various impurities. These can be simply particles of dirt, which lead to turbidity of the water or cause unpleasant odors, such as chlorine. There can also be dangerous bacteria like Escherichia coli. That is why in many regions, water is disinfected by chlorination, thus destroying dangerous pathogens. The drawback of chlorination is on the one hand the resulting odor, on the other hand a reaction of chlorine with organic substances present in water can form harmful by-products such as the carcinogenic trihalomethanes.

Representative for these different pollutants, the model refers to chlorine and the trihalomethane chloroform. The term “particles” covers all substances that are filtered out of the water based solely on their size.

Model Definition

The model geometry is shown in Figure 1. The geometric properties are listed in Table 1.

Figure 1: Sketch of the modeled filter.

Tap water containing different impurities enters the filter with an inlet pressure of pin=6 psi. First, the water passes through the fine pored ceramic, in which particles with a larger diameter than the pore size are filtered out. The fracture in the ceramic has a relatively large aperture such that particles can travel almost unhindered and enter the activated carbon part.

Table 1: Geometry Parameters
Name	Value	Description
r_filter	2.2 cm	Filter radius
l_filter	14.5 cm	Filter length
th_ceramics	0.8 cm	Thickness ceramics
th_carbon	1 cm	Thickness carbon
th_attachement	4 mm	Thickness mount

Activated carbon has a large surface area and is mostly used in granular form in domestic water filters. The advantage of granular-activated carbon compared to powdered-activated carbon is the smaller pressure drop due to its relatively large particle size. At the same time this results in a smaller surface area available for reaction and adsorption. The effect on the adsorption capacity of trihalomethanes like chloroform is similar. The activated carbon is thus used up over time, which makes regular replacement of the filter necessary. In large filter systems the activated carbon can be backwashed.

Fluid Flow

The flow velocity u (SI unit: m/s) through the filter depends on the gradient of the pressure p (SI unit: Pa) as described by Darcy’s law.

Here, κ (SI unit: m2) and μ (SI unit: Pa·s) are the permeability of the filter and dynamic viscosity of water, respectively. For the ceramic part a fixed value for the permeability is assumed and the permeability for the activated carbon is calculated according to the Kozeny–Carman equation.

The flow in the fracture is in general much faster than in the surrounding porous matrix. The cubic law is a common correlation for modeling fracture flow. It defines the permeability κf (SI unit: m2) in the fracture according to

The values used to set up Darcy’s law for the different sections are listed in Table 2.

Table 2: Darcy’s Law Parameter
Name	Value	Description
por_ceramics	0.18	Porosity, ceramics
por_carbon	0.45	Porosity, activated carbon
por_fracture	0.7	Porosity fracture
df	0.2 mm	Fracture aperture
dp_carbon	20 μm	Granular carbon diameter
kappa_ceramics	8·10-12 m2	Permeability ceramics
p_in	6 psi	Inlet pressure

Contaminant transport

Precise values of reaction of chlorine and adsorption rates of chloroform must be measured for each type of activated carbon. Adsorption is modeled using a Freundlich adsorption isotherm. The values used in this model are listed in the Table 3.

Table 3: Transport properties
Name	Value	Description
R_cl	0.391/s	Reaction rate chlorine
S_cp	-0.16 1/s	Particle sink term
Kf	10	Freundlich constant, chloroform
Nf	2	Freundlich exponent, chloroform
cref_chcl3	0.5 mol/m3	Reference concentration, chloroform

The simulation covers a period of two minutes. Afterward, a quasi-stationary state is reached and the filter efficiency can be determined.

Results and Discussion

The pressure and velocity field is shown in Figure 2.

Figure 2: Pressure distribution (color) and flow field (arrows).

The particle concentration after 2 minutes is shown in Figure 3. One can see that the particles are filtered out immediately at the surface. It is mainly the fracture that allows the particles to pass the filter.

Figure 3: Particle concentration in the filter.

Figure 4 shows the chlorine concentration after 2 minutes. After chlorine has passed the ceramic part, it is removed from the water by the reaction with activated carbon.

Figure 4: Chlorine concentration after 2 minutes.

The concentration of dangerous chloroform is shown in Figure 5. It clearly shows that this filter is not suitable for the removal of chloroform. Usually, trihalomethanes are already filtered in the waterworks, with a very strict upper limit — often 0.

Figure 5: Chloroform concentration after 2 minutes.

To evaluate the performance of this filter, we evaluate the ratio between the concentration at the outlet and the concentration at the inlet as shown in Figure 6.

Figure 6: Effectiveness of the filter. Ratio of the concentration at the outlet to the initial concentration.

Notes About the COMSOL Implementation

In this model it is assumed that the flow field does not depend on the species concentrations. This is a reasonable assumption for the time interval considered. If the filter is examined over a long period of time, the particles clog the pores of the ceramic, which leads to a higher pressure drop. In addition, the activated carbon is used up, which means that less chlorine and chloroform is removed.

The fracture in the ceramic filter is implemented as a surface within the 3D domain. This is possible due to the special boundary conditions that are available for the Darcy’s Law and the Transport of Diluted Species interface. They make it possible to simplify the model geometry to save computational resources.

Reference

1. https://www.freshwatersystems.com/blogs/blog

Porous_Media_Flow_Module/Solute_Transport/ceramic_water_filter

Modeling Instructions

Root

Start by opening a file that already contains the geometry sequence as well as selections that are used for setting up the physics. The file also contains all important parameters, divided into three parameter lists for a better overview.

From the menu, choose .

Browse to the model’s Application Libraries folder and double-click the file ceramic_water_filter_geom_sequence.mph.

Geometry 1

Materials

Continue with adding the materials. Water is used from the built-in material library. All other materials are user defined.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Ceramics

In the window, under right-click and choose .

In the window for , type Ceramics in the text field.

Locate the section. From the list, choose .

Activated carbon

Right-click and choose .

In the window for , type Activated carbon in the text field.

Locate the section. From the list, choose .

Fracture

Right-click and choose .

In the window for , locate the section.

From the list, choose .

In the text field, type Fracture.

Which material properties are required will be determined during the physics setup. Continue with defining the Darcy’s Law and Transport of Diluted Species in Porous Media interfaces.

Add Physics

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the tree, select .

Click in the window toolbar.

The geometry also contains the mount, which is not relevant for the simulation. Each interface should be active on the modeling domains only.

Darcy’s Law (dl)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Fluid and Matrix Properties 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Fluid and Matrix Properties 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the dp text field, type dp_carbon.

Fracture Flow 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Fluid and Fracture Properties 1

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

From the list, choose .

Aperture 1

In the window, click .

In the window for , locate the section.

In the df text field, type df.

Pressure 1

A pressure of 6psi is assumed as inlet condition. This is a typical value for the pressure acting on a filter connected to the water supply.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the p0 text field, type p_in.

Pressure 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Transport of Diluted Species in Porous Media (tds)

In the window, under click .

The transport of three different substances is studied: particles which are filtered in the ceramic due to their size, chlorine which reacts with the activated carbon, and chloroform which is adsorbed by the activated carbon.

In the window for , locate the section.

From the list, choose .

Add the corresponding variables for the different compounds.

Click to expand the section. In the text field, type 3.

In the table, enter the following settings:


c_p
c_cl
c_chcl3

Fluid 1

In the window, under click .

In the window for , locate the section.

From the u list, choose .

Duplicate this node and define the adsorption properties of chloroform on activated carbon.

Porous Medium 2

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Adsorption 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Select the check box.

In the KF,cchcl3 text field, type Kf.

In the NF,cchcl3 text field, type Nf.

In the cref,cchcl3 text field, type cref_chcl3.

Species Source 1

The filtration of the particles can be described as a sink term. In contrast, chlorine and chloroform are not removed.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the Scp text field, type S_cp*c_p.

Reactions 1

Chlorine is removed from the water by a reaction with carbon.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the Rccl text field, type -R_cl*c_cl.

Fracture 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the dfr text field, type df.

Locate the section. From the u list, choose .

Locate the section. From the list, choose .

Concentration 1

To complete the physics setup add the boundary conditions for the transport equations.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Select the check box.

In the c0,cp text field, type c_p0.

Select the check box.

In the c0,ccl text field, type c_cl0.

Select the check box.

In the c0,cchcl3 text field, type c_chcl30.

Outflow 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Now the missing material properties can be added.

Materials

Ceramics (mat2)

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Porosity	epsilon	por_ceramics	1	Basic
Permeability	kappa_iso ; kappaii = kappa_iso, kappaij = 0	kappa_ceramics	m²	Basic