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Abstract Dynamic pore‐network model (PNM) has been widely used to model pore‐scale two‐phase flow. Numerical algorithms commonly used for dynamic PNM including IMPES (implicit pressure explicit saturation) and IMP‐SIMS (implicit pressure semi‐implicit saturation) can be numerically unstable or inaccurate for challenging flow regimes such as low capillary number (Ca) flow and unfavorable displacements. We perform comprehensive analyses of IMPES and IMP‐SIMS for a wide range of flow regimes under drainage conditions and develop a novel fully implicit (FI) algorithm to address their limitations. Our simulations show the following: (1) While IMPES was reported to be numerically unstable for lowCaflow, using a smoothed local pore‐body capillary pressure curve appears to produce stable simulations. (2) Due to an approximation for the capillary driving force, IMP‐SIMS can deviate from quasi‐static solutions at equilibrium states especially in heterogeneous networks. (3) Both IMPES and IMP‐SIMS introduce mass conservation errors. The errors are small for networks with cubic pore bodies (less than 1.4% for IMPES and 1.2% for IMP‐SIMS). They become much greater for networks with square‐tube pore bodies (up to 45% for IMPES and 46% for IMP‐SIMS). Conversely, the new FI algorithm is numerically stable and mass conservative regardless of the flow regimes and pore geometries. It also precisely recovers the quasi‐static solutions at equilibrium states. The FI framework has been extended to include compressible two‐phase flow, multicomponent transport, and phase change dynamics. Example simulations of two‐phase displacements accounting for phase change show that evaporation and condensation can suppress fingering patterns generated during invasion.