Near-well simulation in 3D

Accurate and efficient simulation of multiphase flow in the near-well region is a challenging task, due to among others, complex gridding, difference in scale between well-bore radius and reservoir extent, logarithmic pressure behavior, and permeability heterogeneity and anisotropy.

Consider, e.g. a 2D near-well cross-section orthogonal to the well-bore trajectory. For a vertical well this region is usually homogeneous, however, for horizontal or slanted wells passing through sedimentary layering, a heterogeneous near-well region will arise.

Other factors that require a true three-dimensional picture are:

• anisotropy where no principal direction is parallel with the well trajectory
• inhomogeneous fluid saturation distribution along the well,
• pressure loss in the well, and
  gravity.

In this project, we focus on determining a preferred gridding and discretization scheme for near-well simulation in 3D.

Considering first the single-phase case, our starting point will be the well-established multi-point flux approximations (MPFA). Prior numerical testing in 2D have revealed that a logarithmic grid refinement towards the well is necessary for convergence. The refinement was carried out with triangular and quadrilateral element, and it the test indicated that the O-method on triangular elements was the most accurate method.
It was also observed that the L-method did not work well on triangular grids.

In 3D we build general unstructured near-well grids. We investigate tetrahedrons, prisms, pyramids and hexahedrons with or without hanging nodes. On these grids families of MPFA O- and L-methods are tested against analytical solutions, for different values of parameters, e.g., grid cell aspect ratio, permeability anisotropy and heterogeneity. Important properties of the numerical solution are accuracy, convergence rate, and monotonicity.

After finishing a study of the single-phase case, we will extend our investigations to the multiphase case.