Coupled reservoir flow and geomechanics receives a growing research interests for applications in unconventional oil & gas recovery and geological CO2sequestration. For CO2 sequestration, accurate prediction of the behavior of the injected CO2 is important to the long-term success of the sequestration because even small leakage rates over long time periods can unravel the positive outcomes of net CO2 sequestered. Furthermore, the effect of high rates of injection of CO2 on natural fractures is crucial in determination of earthquake effects. High fidelity multiphysics models are needed to simulate these processes and their interactions accurately and efficiently to ensure the success and safety of the operations. Coupled flow-geomechanics simulations are computationally expensive and most of the computational time is usually spent on geomechanics updates. We present a three-way coupling algorithm for both single phase flow and compositional flow coupled with linear poroelasticity. An error indicator is calculated at each flow time step to determine when displacement must be updated and whether fixed-stress iterative coupling technique is required. Convergence of the three-way coupling is established by extending previous work on a priori analyses of fixed-stress iterative coupling. Numerical results for Mandel’s problem confirm these theoretical results for single phase flow. Numerical results for coupled compositional flow and geomechanics simulations for field-scale CO2sequestration and surfactant-alternating-gas (SAG)-assisted CO2 sequestration achieve a substantial reduction in mechanics update times for 99.4% and 97.5%, respectively.