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The existence of large-data weak entropy solutions to a nonisothermalimmiscible compressible two-phase unsaturated flow model in porous media isproved. The model is thermodynamically consistent and includes temperaturegradients and cross-diffusion effects. Due to the fact that some terms from thetotal energy balance are non-integrable in the classical weak sense, weconsider so-called variational entropy solutions. A priori estimates arederived from the entropy balance and the total energy balance. The compactnessis achieved by using the Div-Curl lemma.

Nonisothermal Richards flow in porous media with cross diffusion