Upscaling

OPM Upscaling is a collection of tools for single-phase and steady-state upscaling of capillary pressure and relative permeability.

Illustration of upscaling. The left figure shows averaging of porosity within a model that contains two facies. The right figures shows steady-state upscaling of relative permeability for a bed model.
Illustration of upscaling. The left figure shows averaging of porosity within a model that contains two facies. The right figures shows steady-state upscaling of relative permeability for a bed model.

Single-phase upscaling:

  • flow-based method that uses directional flow problems
  • fixed, linear, or periodic boundary conditions
  • consistent spatial discretization (mimetic finite differences) reduces grid-orientation effects
  • linear solver: algebraic multigrid
  • produces symmetric tensor (with periodic boundary conditions)

Elastic parameters:

  • Algebraic multigrid and overlapping Schwarz preconditioner

Relative permeability and capillary curves:

  • first: computes steady-state by solving two-phase, incompressible, immiscible flow with capillary and gravity forces
  • then: computes effective permeability for given phase mobilities
  • generally gives full tensor relative permeability
  • same pressure solver as in single-phase upscaling (mimetic, AMG)
  • transport solver: two-point, mobility-weighted upwind scheme, explicit or implicit temporal discretization

Electrical resistivity/conductivity:

  • Initialisation of saturations using capillary equilibrium
  • Resistivity/conductivity properties is populated using Archie’s law
  • Resistivity/conductivity is homogenized using Ohm’s law

Upscaling utility (cp-chop):

  • chops a corner-point model into coarse blocks
  • upscales individual blocks in parallel