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Computation of two-phase flow in porous media with low capillary numbers is challenging due to slow convergence and the presence of spurious currents at the phase interfaces that are greater than the viscous flow. The relative permeability of such systems is a critical parameter for upscaling flow properties but requires steady state flow configurations at low capillary numbers; a computationally slow problem to calculate. By using a morphologically coupled multiphase Lattice Boltzmann Method (LBM), it is observed that phase distributions converge an order of magnitude faster (1,000-50,000 timesteps) than flow fields (250,000-350,000 timesteps) during capillary dominated regimes. The proposed method couples a quasi-static, morphological method with direct LBM simulation that combines the efficiency of morphological calculations with the accuracy of direct simulation. The system fluid distribution is initialised …