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The binary-driven hypernova (BdHN) model has been introduced in the past years, to explain a subfamily of gamma-ray bursts (GRBs) with energies Eiso ≥ 1052 erg associated with type Ic supernovae. Such BdHNe have as progenitor a tight binary system composed of a carbon-oxigen (CO) core and a neutron star undergoing an induced gravitational collapse to a black hole, triggered by the CO core explosion as a supernova (SN). This collapse produces an optically-thick e+e- plasma, which expands and impacts onto the SN ejecta. This process is here considered as a candidate for the production of X-ray flares, which are frequently observed following the prompt emission of GRBs. In this work we follow the evolution of the e+e- plasma as it interacts with the SN ejecta, by solving the equations of relativistic hydrodynamics numerically. Our results are compatible with the Lorentz factors estimated for the sources that produce the flares, of typically Γ ≲ 4.