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Title: An Exact Solution of Transport in Porous Media with Equilibrium and Kinetic Reactions

Abstract

This paper presents an analytical solution of reactive transport with equilibrium and kinetic reactions. A benchmark model of A {leftrightarrow} B {leftrightarrow} C {yields} chain reactions is developed for the purpose of verifying numerical computer codes and qualifying mathematical models. A reaction matrix is derived for both the equilibrium and first-order kinetic reactions and further decoupled as a diagonal matrix. Therefore, the partial differential equations (PDEs) coupled by the reaction matrix can be transformed into independent PDEs, for which closed-form solutions exist or can be derived. The analytical solution derived in this paper is compared with numerical results.

Authors:
;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
936682
Report Number(s):
UCRL-JRNL-220600
Journal ID: TPMEEI; TRN: US200818%%1000
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Resource Relation:
Journal Name: Transport in Porous Media, vol. 72, no. 2, March 1, 2008, pp. 199-206; Journal Volume: 72; Journal Issue: 2
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 99 GENERAL AND MISCELLANEOUS; ANALYTICAL SOLUTION; BENCHMARKS; CHAIN REACTIONS; COMPUTER CODES; EXACT SOLUTIONS; KINETICS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; TRANSPORT

Citation Formats

Lu, X, and Sun, Y. An Exact Solution of Transport in Porous Media with Equilibrium and Kinetic Reactions. United States: N. p., 2006. Web.
Lu, X, & Sun, Y. An Exact Solution of Transport in Porous Media with Equilibrium and Kinetic Reactions. United States.
Lu, X, and Sun, Y. Wed . "An Exact Solution of Transport in Porous Media with Equilibrium and Kinetic Reactions". United States. doi:. https://www.osti.gov/servlets/purl/936682.
@article{osti_936682,
title = {An Exact Solution of Transport in Porous Media with Equilibrium and Kinetic Reactions},
author = {Lu, X and Sun, Y},
abstractNote = {This paper presents an analytical solution of reactive transport with equilibrium and kinetic reactions. A benchmark model of A {leftrightarrow} B {leftrightarrow} C {yields} chain reactions is developed for the purpose of verifying numerical computer codes and qualifying mathematical models. A reaction matrix is derived for both the equilibrium and first-order kinetic reactions and further decoupled as a diagonal matrix. Therefore, the partial differential equations (PDEs) coupled by the reaction matrix can be transformed into independent PDEs, for which closed-form solutions exist or can be derived. The analytical solution derived in this paper is compared with numerical results.},
doi = {},
journal = {Transport in Porous Media, vol. 72, no. 2, March 1, 2008, pp. 199-206},
number = 2,
volume = 72,
place = {United States},
year = {Wed Apr 12 00:00:00 EDT 2006},
month = {Wed Apr 12 00:00:00 EDT 2006}
}