Oxygen Transport Under Combustion Conditions in a Fracture-Porous Medium System - Selected Topics of Computational and Experimental Fluid Mechanics - page 338

3 Results and Discussions

For solving Eqs. ( 1 )-( 3 ), along its initial and boundary conditions, we used a finite
element solver ensuring mesh-independent results. For model validation purposes
the experimental concentration profile of a tracer (Rolle et al. 2012 ), that is injected
in a system of porous medium saturated with water, was simulated. An excellent
fitting was obtained. For more details we refer the reader to the work of Rolle et al.
( 2012 ).
In all simulations, we used 300 particles with 0.3mm diameter, and arranged in a
simple periodic array. Such particle diameters are according to those encountered in
combustion tube experiments (Cazarez-Candia et al. 2010 ). In our study, the matrix
porosity was 0.4. The total length of the domain is 10.49mm and the height only
including the porous medium is 3.5137mm, see Table 1 .

3.1 Effect of the Fracture Peclet Number

The effect of the fracture Peclet number (Pe f ) over the non-dimensional oxygen and

coke concentration profiles is illustrated in Fig. 3 ,fort = 25 and 145 s. The plotted

results correspond for diffusive (Pe f = 0:01), competitive (Pe f = 1) and convective

(Pe f = 10) regimes in the fracture. Indeed, a given value of Pe f does not necessarily

mean that such Pe f also stands inside the porous medium. However, we use Pe f ,as
our priority is to investigate the influence that fractures have over the ISC inside the
porous matrix. In our simulations, the manipulation of Pe f was made by increasing
or decreasing the injected flow F inj .
As F inj increases, coke is faster consumed mainly by the increasing oxygen avail-
ability that takes place by two reasons:

Ta b l e 1 Values of some parameters used in the simulations
Parameter Va l u e Reference/comments

10 − 5 kg/(ms 2

μ 1 . 76 × ) at 293.15K White ( 2001 ), Table A.4 O 2

10 − 5 kg/(ms 2 μ 2 . 00 × ) at 293.15K White ( 2001 ), Table A.4 N 2

0.181 cm 2 /s at 273.2K D O 2 Bird et al. ( 2010 ), Table 17.1-1

ʷ 1/1.18 Fadaei ( 2009 ), Table 3.4

Oil API 26

M coke 13.1g/mole Fadaei ( 2009 ), Table 3.3

M oil 290g/mole Fadaei ( 2009 ), Table 3.3

C coke 6,745mol/( a ʽ m 3 ) Based on the assumption that 10% of oil is

converted to coke (Schulte and de Vries 1985 ).
a ʽ is the particle specific surface area