Asal rift is an aerial rift segment resulting from the westward propagation of the Aden ridge into the Afar Depression. Geothermal manifestations such as hot springs and fumaroles, fault creep, conductivity anomaly, and high geothermal gradient were observed both at the surface and in the subsurface. Despite many scientific works conducted in Asal to understand the rifting mechanisms, the hydrothermal fluid circulation still needs to be evaluated since it is based on simplified conceptual models. To further contribute and progress toward a quantitative evaluation of fluid circulation, a 2D numerical model perpendicular to the rift axis was developed with the objective of better understanding the role of subsurface anisotropy in fluid flow and heat transfer in the Asal rift. Numerical modeling of multiphase flow and heat transfer was carried out with an equivalent porous medium intersected by fault zones having greater permeability. Horizontal anisotropic permeability and magmatic fluid release were taken into account with different simulation scenarios. The results indicate that fault zones act as recharge/discharge areas depending on their location, permeability, and number. Simulations considering horizontal anisotropic permeability allowed the reproduction of the thermal state observed in geothermal wells with the expected general pattern of fluid circulation in the Asal rift. Comparing our result with a recent study made with a 2D numerical modeling parallel to the rift axis, we suggest the presence of a saddle point where fluid flow is both to the northeast and to the southwest direction of the rift. Moreover, magmatic fluid release assumed in two simulation scenarios showed to have an impact on the hydrological behavior of fault zones and facilitate the development of super-critical flow at the center of the rift.