This paper presents a mathematical analysis of the evolution of a mixture of two incompressible, isothermal fluids flowing through a porous medium in a three-dimensional bounded domain. The model is governed by a coupled system of convective Brinkman-Forchheimer equations and the Cahn-Hilliard equation, considering a regular potential and non-degenerate mobility. We first establish the existence of a Leray-Hopf weak solution for the coupled system when the absorption exponent
$r\\geq1$. Additionally, we prove that every weak solution satisfies the energy equality for
$r\\geq3$. This further leads to the uniqueness of weak solutions in three-dimensional bounded domains, subject to certain restrictions on the viscosity ($\\\\nu$) and the Forchheimer coefficient ($\\beta$) in the critical case
$r=3$. Similar results are also obtained for the case of degenerate mobility and singular potential.