This study investigates the instability phenomenon during immiscible fluid displacement in a homogeneous porous medium under a magnetic field \(H = \lambda x^{-1}\) , relevant to secondary oil recovery. A nonlinear PDE modeling water saturation ( \(S_\textrm{w}\) ) dynamics was formulated and solved using the hybrid Elzaki Transform Homotopy Perturbation Method (ETHPM). The solution’s convergence was confirmed ( \(\gamma _0 = 0.000350264 < 1\) , \(\gamma _1 = 0.0227059 < 1\) ). Numerical analysis shows that water saturation increases with distance over fixed time intervals, indicating instability development. The magnetic field, characterized by parameter C, significantly enhances this effect, leading to higher saturation rates at greater distances. These findings demonstrate the substantial impact of magnetic fields on fluid displacement, offering insights for optimizing MHD-assisted oil recovery strategies. The successful application of ETHPM highlights its effectiveness for analyzing such nonlinear transport phenomena.
