Author:
CHEN CHING-YAO,MEIBURG ECKART
Abstract
A detailed two-part computational investigation is conducted into
the dynamical
evolution of two-dimensional miscible porous media flows in the quarter
five-spot
arrangement of injection and production wells. High-accuracy direct numerical
simulations
are performed that reproduce all dynamically relevant length scales in
solving
the vorticity–streamfunction formulation of Darcy's law. The
accuracy of the method
is demonstrated by a comparison of simulation data with linear stability
results for
radial source flow.Within this part, Part 1 of the present investigation, a series of simulations
is
discussed that demonstrate how the mobility ratio and the dimensionless
flow rate denoted
by the Péclet number Pe affect both local and integral
features of homogeneous
displacement processes. Mobility ratios up to 150 and Pe-values
up to 2000 are investigated.
For sufficiently large Pe-values, the flow near the injection
well gives rise to a
vigorous viscous fingering instability. As the unstable concentration front
approaches
the central region of the domain, nonlinear interactions between the fingers
similar to
those known from unidirectional flows are observed, such as merging, partial
merging,
and shielding, along with secondary tip-splitting and side-branching instabilities.
At
large Pe-values, several of these fingers compete for long times,
before one of them
accelerates ahead of the others and leads to the breakthrough of the front.In contrast to unidirectional flows, the quarter five-spot geometry
imposes both an
external length scale and a time scale on the flow. The resulting spatial
non-uniformity
of the potential base flow is observed to lead to a clear separation in
space and time
of large and small scales in the flow. Small scales occur predominantly
during the
early stages near the injection well, and at late times near the production
well. The
central domain is dominated by larger scales.Taken together, the results of the simulations demonstrate that both
the mobility
ratio and Pe strongly affect the dynamics of the flow. While some
integral measures,
such as the recovery at breakthrough, may show only a weak dependence on
Pe for
large Pe-values, the local fingering dynamics continue to change
with Pe.The increased susceptibility of the flow to perturbations during the
early stages
provides the motivation to formulate an optimization problem that attempts
to
maximize recovery, for a constant overall process time, by employing a
time-dependent
flow rate. Within the present framework, which accounts for molecular diffusion
but
not for velocity-dependent dispersion, simulation results indeed indicate
the potential
to increase recovery by reducing the flow rate at early times, and then
increasing it
during the later stages.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
116 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献