Premium
A mathematical model for the one‐dimensional transport and fate of oxygen and substrate in a water‐saturated sorbing homogeneous porous medium
Author(s) -
Lindstrom F. Tom
Publication year - 1992
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/92wr00898
Subject(s) - advection , population , eulerian path , substrate (aquarium) , dispersion (optics) , porous medium , sorption , nonlinear system , domain (mathematical analysis) , homogeneous , oxygen , mechanics , thermodynamics , chemistry , mathematics , porosity , physics , mathematical analysis , lagrangian , geology , oceanography , demography , organic chemistry , adsorption , quantum mechanics , sociology , optics
Dissolved oxygen and substrates are transported and processed abiotically and biotically in aquifers. A mathematical model for the one‐dimensional simultaneous transport and fate of dissolved oxygen and substrate in an aerobic water‐saturated linear equilibrium sorption homogeneous porous medium is presented. Transport is by coupled one‐dimensional advection‐dispersion equations. Modified Monod kinetics are used to define the substrate and oxygen utilization rates. The dynamically aerobic microbe population is simultaneously modeled. The resulting coupled system of nonlinear oxygen‐substrate‐microbe population equations is solved via an Eulerian‐Lagrangian method. This is based upon splitting the time operator and using Lagrange cubic splines across the entire domain to solve the advective portion first. The diffusive portion is then solved. An explicit time integration algorithm is sketched. Two numerical validation scenarios are discussed. Three realistic field scenarios are presented based upon published literature kinetic parameters.