Modeling of thermal convection in porous media with volumetric heat source using the GeRa code.

*(Russian. English summary)*Zbl 1437.65165Summary: 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 M. Haajizadeh et al. [Int. J. Heat Mass Transfer 27, 1893–1902 (1984; Zbl 0553.76078)].

In the fifth section we present the results of modelling with GeRa the experiments of R. J. Buretta and A. S. Berman [“Convective heat transfer in a liquid saturated porous layer”, ASME J. Appl. Mech. 43, No. 2, 249–253 (1976; doi:10.1115/1.3423818)] 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 Rayleigh 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.

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 M. Haajizadeh et al. [Int. J. Heat Mass Transfer 27, 1893–1902 (1984; Zbl 0553.76078)].

In the fifth section we present the results of modelling with GeRa the experiments of R. J. Buretta and A. S. Berman [“Convective heat transfer in a liquid saturated porous layer”, ASME J. Appl. Mech. 43, No. 2, 249–253 (1976; doi:10.1115/1.3423818)] 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 Rayleigh 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.

##### MSC:

65N08 | Finite volume methods for boundary value problems involving PDEs |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

76S05 | Flows in porous media; filtration; seepage |

80A19 | Diffusive and convective heat and mass transfer, heat flow |

86A05 | Hydrology, hydrography, oceanography |

35B40 | Asymptotic behavior of solutions to PDEs |

35Q86 | PDEs in connection with geophysics |

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\textit{F. V. Grigoriev} et al., Chebyshevskiĭ Sb. 18, No. 3(63), 235--254 (2017; Zbl 1437.65165)

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