Page 106 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

4.3 Application Examples of the Term Splitting Algorithm 93

muscovite within the time frame considered, the accumulation of quartz exceeds
the consumption of quartz and therefore, the generalized concentration of quartz
increases with time due to both the K-feldspar and muscovite dissolution reac-
+
tions. In the case of the conventional concentration of K , its maximum values
3
3
11
9
are 0.1032 kmol/m and 0.1942 kmol/m at t = 3 × 10 s and t = 1.5 × 10 s
respectively. This indicates a significant increase in the conventional concentration
of K + with the increase of time within the scope of this study. However, in the
case of the conventional concentration of H , its maximum value is a constant of
+
9
3
11
−3
6.4 × 10 kmol/m at both t = 3 × 10 s and t = 1.5 × 10 s. The reason for this
is due to a continuous injection of H at the left entrance of the aquifer. In the case
+
of the generalized concentration of quartz, its maximum values are 0.4051 kmol/m 3
11
3
9
and 0.4067 kmol/m at t = 3×10 s and t = 1.5×10 s respectively. This indicates
a slight increase in the generalized concentration of quartz with the increase of time
within the scope of this study.
Figure 4.8 shows the porosity variation, (φ − φ 0 )/φ 0 , in the fluid-rock interac-
tion system at four different time instants. It is clear that the porosity of the porous
medium evolves with time in the process of fluid-rock interactions. The evolution of
porosity mainly depends on the evolution of the K-feldspar dissolution, muscovite
precipitation and dissolution and pyrophyllite precipitation in the fluid-rock interac-
tion system. In addition, the porosity variation front propagates from the left side to
the right side of the aquifer, which is identical to the direction of pore-fluid flow in
the aquifer. The propagation of the porosity variation front can be clearly observed
from the numerical results shown in Fig. 4.8.
In summary, the related numerical solutions from an application example, which
is a K-feldspar dissolution problem in a pore-fluid saturated, isothermal and homo-
geneous aquifer, have demonstrated that: (1) There exist only a dissolution propaga-
tion front for K-feldspar and a precipitation propagation front for pyrophyllite, but
there exist a precipitation propagation front and a dissolution propagation front for
muscovite during the heterogeneous chemical reactions in the aquifer. (2) The dis-
solution of K-feldspar and muscovite may take place simultaneously in the aquifer
so that pyrophyllite can be precipitated at the early stage of the heterogeneous chem-
ical reactions. (3) All the propagation fronts of chemically reactive species are com-
prised of vertically parallel lines, the propagation directions of which are exactly
the same as that of the pore-fluid flow in the aquifer. (4) The evolution of porosity
mainly depends on the evolution of K-feldspar dissolution, muscovite precipitation
and dissolution and pyrophyllite precipitation in the fluid-rock interaction system.