POLYMIN - University of Waterloo

POLYMIN 2005
Solution Strategy
POLYMIN uses two-step sequential physical-chemical coupling (Walter et al, 1994a) to solve
the reactive transport equations. In this approach, the transport equation is split into a physical
step, and a chemical step:
Step 1 (physical)
n+1 phys
equil
( C k - Ck
) δ(t + ∆t)= Rk
δ(t + ∆t)
k = 1,...,N c
(18)
Step 2 (chemical)
( C
- C
∆t
phys
k
n
k
)
= L( C
k
)
n+1/2
k = 1,...,N
c
(19)
where C k phys is the concentration of component k at the end of the physical step, L represents the
transport operator, δ is the Dirac delta, and n, n+1/2, n+1 relate to the beginning, midpoint, and
end of the time step ∆t, respectively.
The transport model is coupled to the oxygen diffusion and pyrite oxidation modules following
the sequence shown in Figure 1. The simulation over a transport time step ∆t begins with an
iterative solution to the oxygen diffusion and reactive core equations which liberates H + , SO 4 2+ ,
Fe 2+ and Fe 3+ . Because of the nonlinearity for these coupled reactions, the solution is performed
over a smaller sub-time step ∆t oxid , typically 1/10 th - 1/50 th of the transport time step ∆t. These
calculations are very rapid and do not significantly affect the total execution time. The reactive
products are accumulated over each sub-time interval and are added to the existing nodal
concentrations just before the chemical equilibration step.
Following convergence of the diffusion and reactive core equations, a second iterative sequence
begins for the physical/chemical steps. The accumulated oxidation products are added to C k
phys
following the transport step. The equilibrium chemical step is completed independently for each
grid node. An option is available for automatically bypassing this step if the changes in
concentration from the transport and oxidation steps are below a threshold. Typically, the
transport and chemical steps account for approximately 1/3 rd and 2/3 rd of the total execution
time, respectively. Execution times for a 50-year, 13,657-node simulation using a Pentium IV,
3.3Ghz machine were on the order of 40 hours.
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