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We present a conservative smoothed particle hydrodynamics (SPH) model to study the flow of multiple, immiscible fluid phases in porous media using direct pore-scale simulations. Particular focus is put on continuously tracking the evolution of interfacial areas, which are considered to be important morphological quantities affecting multiphase transport in porous media. In addition to solving the Navier–Stokes equations, the model accounts for the effects of capillarity at interfaces and contact lines. This is done by means of incorporating the governing interfacial mass and momentum balances using the continuum surface force (CSF) method, thus rendering model calibration routines unnecessary and minimizing the set of constitutive and kinematic assumptions. We address the application of boundary conditions at rigid solid surfaces and study the predictive capability of the model as well as optimal choices for numerical parameters using an extensive model validation procedure. We demonstrate the applicability of the model to simulate multiphase flows involving partial wettability, dynamic effects, large density ratios (up to 1000), large viscosity ratios (up to 100), as well as fragmentation and coalescence of fluid phases. The model is used to study the evolution of fluid–fluid interfacial areas during saturation-controlled primary drainage and main imbibition of heterogeneous pore spaces at low capillary numbers. A variety of pore-scale effects, such as wetting phase entrapment and fragmentation due to snap-off, are observed. Specific fluid–fluid interfacial area is observed to monotonically increase during primary drainage and hysteretic effects are apparent during main imbibition.