The Johnson-Champoux-Allard-Lafarge (JCAL) model, a pivotal framework in acoustics for analyzing sound absorption in fibrous materials, presents challenges in practical implementation due to its complexity. This paper introduces a refined variant of the JCAL model explicitly tailored for fibrous materials, aiming to balance accuracy and computational efficiency. The proposed model retains essential physical principles while simplifying computational intricacies, enhancing its usability for real-time applications and large-scale simulations. Through comprehensive validation against experimental data, we demonstrate the efficacy of the simplified model in accurately characterizing the sound absorption behavior of fibrous materials. This study contributes to advancing the practical applicability of the JCAL model, facilitating its broader adoption across various acoustic engineering domains. The proposed simplification approach holds promise for accelerating research and development in sound absorption materials and acoustic design methodologies within scientific and engineering communities.