Measured data

Due to the fast convective flow in the crack, the concentration changes in the reservoirs are much faster than for an uncracked specimen (Fig. 5.10). Fig. 5.27 gives the measured data both for a vertical crack of 212 µm and for a vertical crack of 266 µm in a ceramic brick (Table 5.3).

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12 14

Time (days)

Conc (M NaCl)

measured data simulated data 212 µm

266 µm

Fig. 5.27 The measured and simulated concentrations in the reservoirs near a vertically cracked brick with a crack width of 212 µm respectively 266 µm

The measurements of the concentration in the reservoirs give no information about the concentrations in the brick itself. Experimental determination of the concentration in the pore solution in the brick is necessary to validate the simulation of the transport in the brick matrix. Simulations showed that the slower transport through the matrix has no significant contribution to the concentration changes in the reservoirs.

A chemical analysis is performed on the cracked brick with a crack width of 266 µm after 5.5 days of testing in the cells. Based on the study concerning the salt analysis, samples of about 3.0 g of brick are used. When taking into account the density this corresponds to volumes of approximately 1.5 cm³. The sample is cut into 27 pieces, 3 by 3 by 3 in each direction. Results of the chemical analysis of the 27 pieces are given in Fig. 5.29.

Besides the measured concentrations for each piece of brick, the possible range in which these values could lay due to measurement errors is also mentioned. Each value is plotted in vertical surfaces 3 by 3, parallel to the cracked surface: surface (1) represents the brick pieces next to the crack, surface (2) corresponds to the central surface and surface (3) shows values for the surface the most far away from the crack surface. On the left side of the surfaces the high concentration reservoir is situated and on the right side the low concentration reservoir. In the crack rotational convective fluxes are present. At the left the solution at high concentration enters the crack at the bottom, while at the right the solution (at low concentration) enters the crack at the top. This set of boundary conditions results in a complex entity of fluxes inside the sample visible in the concentration distribution (Fig. 5.29).

Before analysing these concentration distributions the main transport phenomena for the cracked brick are visualised in Fig. 5.28. The transport in cracked brick material consists of both fast diffusion-convection transport in the crack and slower transport in the brick matrix. The transport is essentially 3 dimensional incorporating diffusion, convection and gravity forces. The main transport flows are shown in Fig. 5.28. A concentration front moves slowly from the reservoir with the high concentration to the reservoir with the low concentration over the whole surface due to diffusion (Fig. 5.28a). This front moves about three times faster into the crack. Dominating convective fluxes (Fig. 5.28b) are mainly present at the bottom of the front side and in the opposite direction at the top.

Also here the velocity is larger inside the crack, but in this case the difference in velocity is much more pronounced. The salt solution in the crack forms a source for the neighbouring brick material, from which fluxes enter the matrix. The main transport form here is diffusion (Fig. 5.28c). Finally, an important transport of salt takes place later during the experiment in reservoir B back to the matrix. As a result of the high concentrations in reservoir B, caused by the fast convective transport through the crack, there is a driving concentration potential towards the matrix, which is still at a lower salt concentration.

(c)

(a) (b)

x y z

A

Diffusion in the main transport direction B

Convection in the main transport direction

Diffusion perpendicular to the main transport

direction out of the crack into the material Diffusion in the material out of the reservoir at the back side

(d)

Fig. 5.28 Main transport phenomena for a cracked brick

Knowing the main transport phenomena, the concentration distributions can be analysed. In the first surface (1) traces of the rotational flow in the crack are visible mainly due to diffusion into the material. Because the cell test ran already for 5.5 days, the concentration in the right reservoir increased. Higher concentrations entered at the top at the backside of the crack. Consequently, locally higher concentrations (345 mol/m³ NaCl) can be detected compared to the middle of the brick (281 mol/m³ NaCl). More inside the material (Fig. 5.29 middle and right), the influence of the crack is decreasing. The concentration changes inside the brick are mainly caused by diffusion:

the thickness and the small permeability (5x10^-9 s) of the brick limit convection. The permeability of the tested cracks is around 5x10^-3 s. Consequently, the convective transport is taking place mainly in the crack. Next to diffusion driven by the high concentrations in the crack, diffusive transport from the reservoirs is detectable.

Logically, the concentrations due to transport from the left side are higher than the concentrations due to diffusion transport from the right side.

Vertical surface (1) next to the cracked

surface

Vertical surface (2) in the middle

Vertical surface (3) farthest away from the crack

Fig. 5.29 Concentrations (mol/m³) of the solution in the pores based on the chemical analysis of the brick pieces from the cracked brick with a crack width of 266 µm