<p>This study investigates the role of the elastic energy release rate of a circular region ahead of the crack tip (<i>G</i>-annulus) in hydro-fracking, focusing on the interaction of fluid-driven fractures in a porous medium. We present a thermomechanics perspective characterizing the evolution of dissipative and stored energy release and systematically study the influencing factors using the phase-field method. We first verify our phase-field model of fracture under dry conditions by the double edged crack benchmark which can accurately capture the crack propagation and interaction, demonstrating the model’s capacity for investigating crack interaction. Our findings indicate that the interplay between the energy release rate within the <i>G</i>-annulus and fluid movement determines the dynamics of crack pair intertwining, including crack repulsion and attraction. Specifically, we observe that under the same injection conditions the energy release rate significantly influences the interacting crack pair, with a higher rate leading to a more prominent intertwining attributed to an expansion of the <i>G</i>-annulus. An increased injection rate accelerates fracture propagation and expands the <i>G</i>-annulus size, thus leading to more significant stress-field interactions. Conversely, a higher fluid mobility results in a relatively mild crack coalescence due to a less significant interaction of the stress fields as the fluid pressure distribution around the crack tips is lowered. This work extends its implications to geo-environmental engineering applications such as hydraulic fracturing in geothermal and subsurface CO<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> sequestration projects, as well as potential biomedical engineering research.</p>