Tie-Simplex Parameterization of Operator Based Linearization for Isothermal Multiphase Compositional Flow In Porous Media

Abstract

Compositional flow simulation is the best practise to model the complex enhanced oil recovery process. This involves solving highly coupled and non linear flow, transport equations.
Interaction of components within different phases and the fluid interaction with rock properties makes it difficult to accurately predict the natural flow process in the reservoir. This
demands for resolution models and accurate representation of flow process with realistic assumptions., which is quite challenging with conventional simulation.
The newly proposed Operator based linearization (OBL) approach handles the problem in a
different way. Governing equations are regrouped using state and space operators. The state
operators are computed at the nodes of uniform mesh in parameter space and multi- linear
interpolation is performed during simulation. Uniformly distributed supporting points ignore
the underlying physics leading to higher interpolation error around the phase boundary and
demanding higher resolution to achieve the desired accuracy.
The objective of “Tie simplex parameterization of Operator-Based Linearization for Isothermal
Multiphase Compositional flow in porous media” is to parameterize the compositional space
by accounting the underlying physics. A set of tie lines captures the phase boundary in
parameter space at given pressure and temperature. Tessellation is performed by extending
the tie lines to the entire compositional space. The supporting points are assigned along the
extended tie-lines according to manually designed heuristics. After that, the parameterized
space is tessellated further using Delaunay triangulation, and barycentric interpolation is
performed within each simplex.
The efficiency of the developed approach is demonstrated in comparison with the uniform
parameterization using 1D displacement of compositional two-phase fluid. The convergence
of non linear newton iterative solver is studied by applying the OBL framework with newly
proposed interpolation and existing Multi-Linear interpolation framework.