Reactive flow in porous media plays a crucial role in various fields, including the petrochemical industry, water decontamination, biofilm metabolism, and the medical industry. This study focuses on reactive displacement in heterogeneous porous media involving a chemical reaction, $A + B \rightarrow C$, which serves as a fundamental building block for more complex reactions. Understanding this reaction can provide insights into a broader range of chemical processes. To model this phenomenon, we couple convection-diffusion-reaction equations with the Brinkman equation to account for momentum conservation. Additionally, the heterogeneity of the porous media is captured by modeling its permeability as an exponential function of the product concentration. Due to the inherent nonlinearities, we adopt a variational approach to establish well-posedness for the problem. We obtain various priori estimates using functional analysis tools such as Young`s and Holder`s inequalities. Using these estimates along with the Galerkin method, we establish the existence of a solution. Furthermore, we demonstrate continuous dependence on the initial data, ensuring the uniqueness of the solution