The Marine Unsaturated Model (MARUN model) is a two-dimensional (vertical slice) finite element model capable of simulating the migration of water and solutes in saturated-unsaturated porous media while accounting for the impact of solute concentration on water density and viscosity, as saltwater is heaving and more viscous than freshwater. The detailed formulation of the MARUN model is found in (Boufadel et al. 1998)[1] and (Boufadel et al. 1999).[2] The model was used to investigate seepage flow in trenches and dams (Boufadel et al. 1999,[3] Naba et al. 2002 [4] ), the migration of brine following evaporation (Boufadel et al. 1999) [5] and (Geng and M.C. 2015),[6] submarine groundwater discharge (Li et al. 2008),[7] and beach hydrodynamics to explain the persistence of some of the Exxon Valdez oil in Alaska beaches (Li and Boufadel 2010).[8]
Model formulation
editIn the absence of source/sink terms, the equation for the conservation of the fluid mass (water + salt) is:
where is the porosity of the medium() and S is the water saturation ratio of soil moisture with a value of 1 implying fully saturated soil,
![{\displaystyle \phi \left[-\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0803e9e9d5e1f2bf09e46c2dfd15e37a6d0da2f)
In the absence of source/sink terms, the equation for the conservation of the solute equation is expressed as:
BIOMARUN
editThe model BIO-MARUN resulted from combining the model BIOB (for biodegradation in a block) with the MARUN model. The BIOB model (Geng et al. 2012)[9] and (Geng et al. 2014)[10] requires the concentration of hydrocarbons, the microbial density, and oxygen and nutrient concentrations. It uses Monod kinetics to predict microbial growth, oxygen consumption, and CO2 production. An implementation of the model was also conducted by (Torlapati and Boufadel 2014).[11] The BIOB model can also revert to using default values.
The BIOMARUN model allows tracking of two substrates (or food), two microbial communities, and up to 8 solutes, and it was used to predict oil biodegradation under natural conditions (Geng et al. 2015) [12] and with amendments (i.e., bioremediation) (Geng et al. 2016).[13] The BIOMARUN model was also used to investigate the biodegradation of benzene in tidally influenced beaches (Geng et al. 2016) [14]
TMARUN
editTo account for heat transfer through liquid and vapor transport, the model MARUN was coupled with equations for the migration of heat through conduction and vapor transport as documented closely in (Geng and M.C. 2015,[6] Geng et al. 2016 [15]). The TMARUN model was used to explain the presence of high salinity (100 g/L more than 3 times that of seawater) in the intertidal zone of beaches.
Notes and references
edit- ^ Boufadel, M. C., M. T. Suidan, C. H. Rauch, A. D. Venosa and P. Biswas (1998). "2-D variably-saturated flow: Physical scaling and Bayesian estimation." Journal of Hydrologic Engineering 3(10): 223-231.
- ^ Boufadel, M. C., M. T. Suidan and A. D. Venosa (1999). "A numerical model for density-and-viscosity-dependent flow in two-dimensional variably-saturated media." Journal of Contaminant Hydrology 37: 1-20.
- ^ Boufadel, M., M. Suidan, A. Venosa and M. Bowers (1999). "Steady Seepage in Trenches and Dams: Effect of Capillary Flow." Journal of Hydraulic Engineering 125(3): 286-294.
- ^ Naba, B., M. C. Boufadel and J. Weaver (2002). "The role of capillary forces in steady‐state and transient seepage flows." Groundwater 40(4): 407-415.
- ^ Boufadel, M., M. Suidan and A. Venosa (1999). "Numerical modeling of water flow below dry salt lakes: effect of capillarity and viscosity." Journal of Hydrology 221(1): 55-74.
- ^ a b Geng, X. and B. M.C. (2015). "Numerical modeling of water flow and salt transport in bare saline soil subjected to evaporation." Journal of Hydrology 524: 427-438.
- ^ Li, H., M. C. Boufadel and J. W. Weaver (2008). "Tide-induced seawater–groundwater circulation in shallow beach aquifers." Journal of Hydrology 352(1): 211-224.
- ^ Li, H. and M. C. Boufadel (2010). "Long-term persistence of oil from the Exxon Valdez spill in two-layer beaches." Nature Geoscience 3(2): 96-99.
- ^ Geng, X., M. C. Boufadel and B. Wrenn (2012). "Mathematical modeling of the biodegradation of residual hydrocarbon in a variably-saturated sand column." Biodegradation 24(2): 153-163.
- ^ Geng, X., M. C. Boufadel, Y. Personna, K. Lee and D. Tsao (2014). "BioB: A Mathematical Modeling for the Biodegradation of Low Solubility Hydrocarbons." Marine Pollution Bulletin (In press).
- ^ Torlapati, J. and M. C. Boufadel (2014). "Evaluation of the biodegradation of Alaska North Slope oil in microcosms using the biodegradation model BIOB." Frontiers in Aquatic Microbiology 5(212): 1-15.
- ^ Geng, X., M. C. Boufadel, K. Lee, S. Abrams and M. Suidan (2015). "Biodegradation of subsurface oil in a tidally influenced sand beach: Impact of hydraulics and interaction with pore water chemistry." Water Resources Research.
- ^ Geng, X., Z. Pan, B. M.C., T. Ozgokmen, K. Lee and L. Zhao (2016). "Simulation of oil bioremediation of a tidally-influenced beach: Spatio-temporal evolution of nutrient and dissolved oxygen." Journal of Geophysical Research, Oceans.
- ^ Geng, X., M. C. Boufadel and F. Cui (2016). "Numerical modeling of subsurface release and fate of benzene and toluene in coastal aquifers subjected to tides." Journal of Hydrology.
- ^ Geng, X., M. C. Boufadel and N. Jackson (2016). "Evidence of salt accumulation in beach intertidal zone due to evaporation." Scientific Report 6(31486; doi: 10.1038/srep31486): 1-5.