Riemann Problems for a new class of equations ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Riemann Problems for a new class of equations modeling steam injection with applications in groundwater remediation.
Author:Wanderson Lambert <wanderson.lambert@gmail.com> (IMPA - Instituto de Matemática Pura e Aplicada)
Dan Marchesin <marchesi@fluid.impa.br> (IMPA - Instituto de Matemática Pura e Aplicada)
Presenter:Wanderson Lambert <wanderson.lambert@gmail.com> (IMPA - Instituto de Matemática Pura e Aplicada)
Date: 2006-06-18     Track: General Sessions     Session: General

Groundwater contamination by organic materials and petroleum products is a preoccupying problem with environmental, social and health implications constituting a menace to our high-quality groundwater resources. An important remediation technique is steam injection. The model that we propose to describe this injection is a balance system, because it considers the terms of mass transfer and chemical reactions in the different physical phases. We have developed techniques to solve the Riemann problems associated to the balance system for thermal flow in porous media. This theory was initially studied in [1] and it is extended in [2]. As an example, we analyze the steam and water injection in several proportions into a porous medium saturated with different mixtures of steam, water and small amounts of NAPL’s. One disadvantage of pure steam injection is the ecological impact of high temperatures. This can be alleviated if we co-inject nitrogen leading to a lower temperature, because the boiling temperature depends on nitrogen concentration and it is lower than the boiling temperature for pure water. We consider a one-dimensional porous medium filled with water, where steam and nitrogen are injected. We neglect compressibility, heat losses and capillarity effects and present a physical model for steam injection based on the mass balance and energy conservation equations. We show several Riemann solutions for different physical initial and injection conditions. An interesting feature is that we can calculate the mass transfer directly from the model, without knowing the expression for the mass transfer, see [2] for more details. [1] Bruining, J. and Marchesin, D. , Nitrogen and steam injection in a porous medium with water, to appear to Transport in Porous Media (2006). [2] Lambert, W., Doctoral Thesis, IMPA- 2006, in preparation.