A complex concept of the propagation of fractures in carbonate or shale reservoirs means that their start and propagation during production are not given much consideration. A quantitative measurement of propagation in reservoir simulators is essential. Stochastic data, such as boundary conditions, pressure, viscosity, and other aiming functions, amplify this finding. The regime of multiphase flow further complicates but also challenges the question in terms of formulation. That is precisely the topic of this research, which is to say the crack network configurations as they propagate in time with random inputs, starting with stochastic optimum control. A known issue in fractured rocks is the Brinkman model, which contains parts where the Darcy flow predominates and areas where the Stokes flow predominate. Once we've developed our flow model in fractured rocks, we'll use energy minimization procedures to further refine it. Because of its robustness, our approach takes a little time to calculate. As this handicap is "reduced," it will be easier to put this model into practice at the Darcy scale in the future.