Two-Way Coupling Of Flow And Geomechanics Simulations With Local Grid Refinement
A. Rodriguez, J. Monteagudo and N. Nieto
Event name: ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery
Session: Reservoir Geomechanics
Publication date: 03 September 2018
Info: Extended abstract, PDF ( 2.65Mb )
Price: € 20
Unconventional reservoirs can only be economically exploited via massive stimulation by means of the creation of multiple hydraulic fractures. These systems are mechanically sensitive due to the presence of the hydraulic fractures (which tend to close during depletion), as well as natural and induced shear fractures which constitute the so-called stimulated reservoir volume (SRV). Another factor that contributes to the induced mechanical deformation is the ultra-low permeability of the reservoir rocks. This induces extremely steep pressure gradients in the vicinity of the hydraulic fractures which translate into large mechanical forces, able to locally modify the in-situ stresses as well as other effects such as modification to the formation permeability. Numerical simulation of hydrocarbon recovery in this kind of reservoirs must consider two-way coupling of flow and geomechanics. Another challenge in the simulation of stimulated unconventional reservoirs relates to the localization of pressure gradients around hydraulic fractures. The most efficient way to model and simulate flow in those regions relies on the use of local grid refinement (LGR). LGR, however, poses additional challenges in the implementation of the coupling of flow and geomechanics. In this paper, we propose that this coupling can be achieved by applying a higher integration order to the mechanical equations of LGR gridblocks. Flow equations are usually discretized following a two-point approximation with cell-centered properties. Mechanical equations are solved at the quadrature points which in a Q1 approximation correspond to the corners of the blocks while Q2, Q3 and so on, add additional nodes which correspond to the corners of the LGR cells. The order of the finite element and the LGR discretization can be chosen in a consistent manner. Next, an iterative coupling scheme is used until convergence is achieved. In this paper, we implemented this idea and show that the coupled LGR formulation satisfactorily replicates the reference solutions obtained using a fine grid to represent the volume. The method is validated by comparing the simulation of several examples with analytical and fine-grid solutions.