MODELING OF THERMAL CONVECTION IN POROUS MEDIA WITH VOLUMETRIC HEAT SOURCE USING THE GERA CODE

This article is devoted to the problem of thermal convection in porous media with volumetric heat generation modelling, arising in  practice of radioactive waste (RW) disposal safety assessment. In  the first section a brief overview of widespread hydrogeological  codes (FEFLOW, SUTRA, SEAWAT, TOUGH2) featuring the ability to  solve thermal problems is done. We point out the lack of heat  generation caused by radioactive decay model in these programs.  The GeRa numerical code developed by the authors is presented. In  the second section we consider the mathematical model of coupled groundwater flow, solute and heat transport, which is  implemented in GeRa. The model describes these processes in  saturated porous media and takes into account radioactive decay,  sorption on the rock, the dependences of density and viscosity on  temperature. The heat transport equation is written assuming thermal equilibrium between the fluid and the rock. The model  includes heat transport by convection and conduction-thermal dispersion. The heat source terms can be wells and volumetric heat generation due to radioactive decay. The numerical scheme  implemented in GeRa to solve the aforementioned coupled problem  is introduced in the third section. The space discretization is done  using finite volume methods (FVM). Sequential iterative coupling implicit scheme is used for temporal discretization. On each iteration  of the scheme the flow, heat transport and solute transport problems are solved sequentially. The fourth section is devoted to the test  problem of heat generating fluid convection in a closed two- dimensional cavern filled by porous material with isothermal walls.  The results obtained using GeRa code are compared to the  asymptotical solution deduced by Haajizadeh. In the fifth section we  present the results of modelling with GeRa the experiments of  Buretta and Berman in which they investigated the regimes of free thermal convection of fluid with volumetric heat generation in porous media. The dependences of Nusselt number on the Raley number  measured in the experiments and calculated numerically are  compared. In the sixth section we consider the test problem of  continuous injection of high-level RW into an aquifer. Here the ability to model coupled flow, heat and solute transport processes is shown. The numerical solution obtained using GeRa is compared to a known analytical one.

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