A Lattice Model for Simultaneous Multi-Phase Flow and Matrix Deformation

Sakalima Sikaneta, Lawrence Plug, and Grant D. Wach
Dalhousie University, Halifax, NS

Subsurface formations are composed of a solid matrix and pore-filling fluids. These rheologically distinct materials are typically modelled with separate algorithms, and in many cases only one is considered under the assumption their dynamics are isolated. For example, solid modelling is used to simulate elastic wave propagation for seismic modelling, for well-bore stability, and for retrodicting historical strain rates and most probable locations of natural fractures. Modelling multi-phase flow of fluids within reservoir pore spaces and fractures is of obvious importance to the petroleum industry. In many cases flow and elastic deformation interact, causing a coupling between flow, pore pressure, compaction, and effective stresses. However, the use of separate algorithms to model fluid and solid deformation makes coupled models difficult.

We have adapted a lattice modelling approach from fluid dynamics to simulate the deformation of elastic solids, including fracturing. The algorithm has already been established as a useful tool for multiphase and non-ideal fluid flows in complicated geometries such as pore spaces and fractures within reservoirs. We use the Marmousi-2 synthetic data set to test the lattice model, comparing P-S mode conversion and wave front geometry in the lattice model to a fourth-order finite-difference model. We also present results of modelling simultaneous fracture and fluid flow during the hydraulic fracture of a sandstone, investigating the influence of matrix elasticity, porosity, permeability, and pore fluid viscosity and density on resultant fracture geometry.