This paper presents a comprehensive study on phase-field modelling in COMSOL MultiPhysics for simulating dynamic hydraulic fracturing in porous media based on Biot’s poro-elasticity theory. The focus is on addressing the challenges associated with crack width estimation in this context. A new strain-based crack width formulation is proposed, offering improved accuracy in predicting fracture permeability and ease of implementation in numerical approaches. The model’s capabilities are extended to consider dynamic crack propagation by incorporating the kinetic energy in the governing coupled hydro-mechanical-damage equations. The numerical implementations in COMSOL MultiPhysics are thoroughly explained, providing insights into the techniques used to solve the governing equations. Verification examples, including the benchmark KGD verification, are presented to demonstrate the model’s capabilities in simulating hydraulic fractures in porous media and validate its accuracy and reliability. A final numerical example focusing on the dynamics of crack propagation in a gravity dam is simulated, allowing for a comprehensive examination of the model’s performance. The proposed strain-based crack width formulation and consideration of dynamic crack propagation contribute to improved accuracy in predicting fracture permeability.