Page 242 - Process Modelling and Simulation With Finite Element Methods

Geometric Continuation 229

r

I'
0.8
0.6
0.4
0.2
10 4%
2 4 6 8
Figure 6.9 Absorption isotherm. r = amount of surfactant loading the particle surface. m=l and
yo=3.
model presented here. Trogus et al. [15], in the context of enhanced oil
recovery, proposed a hnetic model for adsorptioddesorption rates, and Ramirez
et al. [16] developed a two-equation (concentration and surfactant loading), 1-D
spatio-temporal model for dynamic adsorption. Nevertheless, their transport
model is still for a homogeneous porous media, where in ours, given below, the
compaction front between the close packed and looser packed layers, serves as
an impetus for desorption, and thus as a propagating point source of surfactant.
Posed for the first time here is a transport model for the surfactant:

where the first term on the LHS represents accumulation of surfactant, the
second part of the factor being due to accumulation in the adsorbed phase; the
second term represents a point source of surfactant being desorbed from the
compaction front; the RHS represents a diffusion term. Since the equation is
dimensionless, the coefficient of the diffusion term represents an inverse Peclet
number:

(6.10)

where D, is the molecular diffusivity of the surfactant, His the initial film depth,
and E is the evaporation rate. The Peclet number is taken as unity for
the purpose of example. In the simulations that follow, it will be vaned
systematically.
Representative values of packings are: Grn = 0.64 Go = 0.4