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Fate of microorganisms in porous media has very important applications in many branches of<br>environmental and petroleum science and engineering, like in the Microbial Enhanced Oil Recovery<br>(MEOR) processes, among others; however, concurrently it is a very complex and interacting phenomenon<br>mainly because microorganisms are living. Applying the systematic modeling approach to continuum<br>systems, we derive a model that include net flux of microorganisms and nutrients by convection and<br>dispersion, growth and decay rates of microorganisms, chemotactic movement and nutrient consumption,<br>adsorption of microorganisms and nutrients on rock grain surfaces, as well as desorption of<br>microorganisms. Porosity reduction due to cell and nutrient adsorption is considered. We implement the<br>model within a Finite Element Method. The numerical simulations reproduce results previously reported<br>elsewhere; moreover, we show the spatial-temporal distribution of microorganisms and nutrients along the<br>system and time. We point out the complementary role of the spatial-temporal distribution of components<br>with breakthrough curves to analyze the behavior of both fluent and adsorbed components.