Oil and gas production projects rely on hydraulic fracturing for improved well stimulation and profitability. Research progress on numerical simulation enables design teams to estimate rock behavior and ensure the success of such operations. Stimulation operations usually take only a few hours, and fluid diffusion around the well is normally unimportant. In long-term improved oil recovery injection projects, however, injected water and gas significantly modify reservoir pore pressure and geomechanical conditions around injection wells. This paper proposes a fully coupled hydromechanical full-field reservoir simulator to consider the effects of such coupled effects in the propagation of tensile hydraulic fractures in short- and long-term processes. The numerical approach uses finite elements to represent the poroelastic medium and lower dimension cohesive interface elements to represent fragile interfaces. Numerical accuracy is validated against asymptotic analytical solutions. The results show significant impact of fluid injection and production history in the attributes of the fracture generated. For long-term projects, designers must avoid the use of off-the-shelf hydraulic fracturing simulators designed typically for stimulation operations. This paper encourages using fully coupled, full-field reservoir simulators and considering, in detail, the variety of physical phenomena present in the process. The main contributions of this work comprise an incremental damage control algorithm for fracture propagation and a geometrical analysis technique for avoiding mesh overlap on damaged compressive interfaces.