The evolution of a geothermal system is studied. A mathematical model is proposed and the corresponding free boundary problem is formulated in a one-dimensional geometry. A situation corresponding to the geothermal field in Larderello, Tuscany (Italy) is considered, showing that the problem has two characteristic time scales, related to the motion of interface and di¤usion of vapor. Since the former is much slower, a quasi-steady approximation can be introduced and solved, obtaining a qualitative description of the evolution of the Larderello basin from a liquid-dominated to a vapor-dominated situation. This is in agreement with the geological results. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.
A free boundary model for the evolution of a geothermal system / l.Meacci,A. Farina, M. Primicerio,. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - STAMPA. - 30:(2019), pp. 125-136. [10.4171/RLM/838]
A free boundary model for the evolution of a geothermal system
A. Farina;M. Primicerio
2019
Abstract
The evolution of a geothermal system is studied. A mathematical model is proposed and the corresponding free boundary problem is formulated in a one-dimensional geometry. A situation corresponding to the geothermal field in Larderello, Tuscany (Italy) is considered, showing that the problem has two characteristic time scales, related to the motion of interface and di¤usion of vapor. Since the former is much slower, a quasi-steady approximation can be introduced and solved, obtaining a qualitative description of the evolution of the Larderello basin from a liquid-dominated to a vapor-dominated situation. This is in agreement with the geological results. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.File | Dimensione | Formato | |
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