Absorption - Introduction to Carbon Capture and Sequestration - page 198

() ( )

j CO 2 z j CO 2 z + dz

z

z + dz

Figure 5.4.3 Mass balance

The accumulation is equal to the increase in the number of molecules
in the volume ( V

= dxdydz ):

dc

CO

accumulation =

2

dxdydz

dt

The fl ow in and out of the volume is given by the fl ux times the area ( A =

dydx ):

fl ow in = j CO 2 (z)dydx

fl ow out = j CO 2 (z + dz)dydx

For the fl ow in minus fl ow out, we can write:

()

dj z

CO

() ( )

j z − j z + dz dydx = −

2

CO CO

dz

2 2

This gives us for the mass balance:

() ()

dc z dj z

CO CO

2

=−

2

dt dz

If we insert Fick's law into this result, we get the following differential
equation for the time-dependent concentration profi le:

()

2

()

dc z d c z

CO CO

2

= D

2

CO

2

dt

2

dz