Modeling reactive transport using exact solutions for first-order reaction networks |
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Authors: | Yunwei Sun Thomas A Buscheck Yue Hao |
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Institution: | (1) Lawrence Livermore National Laboratory, 808, L-631, Livermore, CA 94550, USA |
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Abstract: | Operator splitting is often used for solving advection-dispersion-reaction (ADR) equations. Each operator can be solved separately
using an algorithm appropriate to its mathematical behavior. Although a lot of research has been done in operator splitting
for solving ADR equations, numerical approaches for the reaction operator are computationally expensive. To meet the convergence
criteria of ODE (ordinary differential equation) or DAE (differential algebraic equation) solvers, a transport time step has
to be subdivided into a large number of reaction time steps. Additional computation effort is also required to reduce the
splitting error. In this paper, we develop exact solutions of various first-order reaction networks for the reaction operator
and couple those solutions with numerical solutions of the transport operator. The reactions are treated as local phenomena
and simulated using exact solutions that we develop, while advection and dispersion are treated as global processes and simulated
numerically. The proposed method avoids the numerical error from the reaction operator and requires a single-step calculation
to solve the reaction operator. Compared to conventional operator-splitting methods, the proposed method offers both computational
efficiency and simulation accuracy. |
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Keywords: | Reactive transport First-order reaction Operator splitting Numerical modeling Analytical solution |
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