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5.3 Application of the Segregated Algorithm 115

one among the three propagation fronts, namely a porosity propagation front, a
dimensionless-concentration propagation front and a dimensionless-pressure propa-
gation front, in the computational model. Clearly, the dimensionless-pressure prop-
agation front has the widest bandwidth, implying that it is the least sharp front
in the computational model. Although there are some smoothing effects on the
numerically-simulated propagation fronts as a result of numerical dispersion, the
propagation speed of the numerically-simulated propagation front is in good coinci-
dence with that of the analytically-predicted propagation front. For this benchmark
problem, the overall accuracy of the numerical results is indicated by the dimension-
less pressure. The maximum relative error of the numerically-simulated dimension-
less pressure is 2.2%, 4.6% and 5.8% for dimensionless times of 0.25, 0.625 and 0.8
respectively. If both a small mesh size and a small time step are used, then the max-
imum relative error can be further reduced in the numerical simulation. This quan-
titatively demonstrates that the proposed numerical procedure can produce accurate
numerical solutions for the planar dissolution-front propagation problem within a
fluid-saturated porous medium.

5.3 Application of the Segregated Algorithm for Simulating
the Morphological Evolution of Chemical Dissolution Fronts

In this section, the proposed numerical procedure is used to simulate the morpho-
logical evolution of a chemical dissolution front in a supercritical system. For this

purpose, a dimensionless-pressure gradient (i.e. p =−10) is applied on the left
fx
boundary of the computational domain so that the dimensionless speed of the dis-
solution front propagation is equal to 100. This means that the dissolution front
propagates much faster than it does within the system considered in the previous
section. Due to this change, the ratio of the equilibrium concentration to the solid
molar density of the chemical species is assumed to be 0.001, while the dimension-
less time-step is also assumed to be 0.001 in the computation. The Zhao number of
the system is increased to 10, which is greater than the critical Zhao number (i.e.
approximately 1.77) of the system. The values of other parameters are exactly the
same as those used in the previous section. Since the Zhao number of the system is
greater than its critical value, the coupled system considered in this section is super-
critical so that a planar dissolution front evolves into a complicated morphology
during its propagation within the system. In order to simulate the instability of the
chemical dissolution front, a small perturbation of 1% initial porosity is randomly
added to the initial porosity field in the computational domain.
Figure 5.5 shows the porosity distributions due to the morphological evolution of
the chemical dissolution front in the fluid-saturated porous medium, while Fig. 5.6
shows the dimensionless concentration distributions due to the morphological evo-
lution of the chemical dissolution front within the computational domain. It is
observed that for the values of the dimensionless time greater than 0.03, the ini-
tial planar dissolution front gradually changes into an irregular one. With a fur-
ther increase of the dimensionless time, the amplitude of the resulting irregular