Stochastic modeling of fracture initiation and propagation during fluid flow in carbonate reservoir

Abstract

Fracture initiation and propagation in fractured carbonate reservoirs or shale ones during the production phase of the reservoir goes without paying particular attention because of the complex model that represents in itself the propagation of fracture. It goes without saying how important an assessment of this phenomenon, propagation, would be in quantitative terms for reservoir engineering in reservoir simulators. This fact becomes even more interesting when our data are stochastic, such as boundary conditions, pressure, viscosity, and other targeting functions. Exactly in this paper, we will address such a problem, i.e., the configurations of the crack network as propagating them in time when the inputs are random starting directly with stochastic optimal control Brinkman model in fractured rocks, which is known to be a problem that includes areas where the Darcy flow predominates and areas where the Stokes flow predominates. We will then develop our flow model in fractured rocks under the effects of geomechanical processes by undergoing energy minimization processes. Our method is robust, although at the moment, it requires a bit of calculation time. In the future, the “reduction” of this handicap would pave the way for the implementation of this model on a large Darcy scale.

Keywords

• Stochastic Brinkman optimal control
• Fractured carbonate reservoirs
• Fracture initiation and propagation
• Geomechanical processes
• Fracture energy minimization