TY - EJOU
AU - Sun, Shuyu
TI - Fully Phase-Wise Conservative and Bound-Preserving Algorithms for Multiphase Flow in Geological Formation
T2 - The International Conference on Computational \& Experimental Engineering and Sciences
PY - 2021
VL - 23
IS - 1
SN - 1933-2815
AB - Modeling and simulation of multiphase flow in porous media have
been a major effort in reservoir engineering and in environmental study.
Petroleum engineers use reservoir simulation models to manage existing
petroleum fields and to develop new oil and gas reservoirs, while environmental
scientists use subsurface flow and transport models to investigate and compare
for example various schemes to inject and store CO2 in subsurface geological
formations, such as depleted reservoirs and deep saline aquifers. One well cited
requirement is to conserve the mass globally and locally, but most popular
methods of N-phase flow used in practice conserve mass only for (N-1) phases,
especially with IMPES schemes. Another basic requirement for accurate
modeling and simulation of multiphase flow is to have the predicted physical
quantities sit within a physically meaningful range. For example, the predicated
saturation should sit between 0 and 1 while the predicated molar concentration
should sit between 0 and the maximum value allowed by the equation of state.
Unfortunately, popular simulation methods used in petroleum industries do not
preserve physical bounds. A commonly used fix to this problem is to simply
apply a cut-off operator (say, to the computed saturation) at each time step, i.e.,
to set the saturation to be zero whenever it becomes negative, and to set it to one
whenever it becomes larger than one. However, this cut-off practice does not
only destroy the local mass conservation but it also damages the global mass
conservation, which seriously ruins the numerical accuracy and physical
interpretability of the simulation results. In the talk, we will present two of our
recent work on fully conservative and bound-preserving discretization and
solvers for subsurface flow models, one based on a fully implicit framework and
another one based on an IMPES/IMPEC-type semi-implicit framework. In the
semi-implicit framework, we proposed new decoupling schemes to allow fully
conservative for each phase locally and globally, with bound-preserving
properties with certain time step conditions. In the fully implicit framework, we
reformulated a few subsurface flow models using variational inequalities that
naturally ensure the physical feasibility of the physical quantities including
saturations and concentrations. We applied a mixed finite element method to
discretize the model equations for the spatial terms, and the implicit backward
Euler scheme with adaptive time stepping for the temporal integration. The
resultant nonlinear system arising at each time step was then solved in a
monolithic way by using a Newtonâ€“Krylov type method, where the resultant
nonlinear system was solved by a generalized Newton method, i.e., active-set
reduced-space method, and then the ill-conditioned linear Jacobian systems were
solved with an effective preconditioned Krylov subspace method. The used
nonlinear preconditioner was built by applying overlapping additive Schwarz
type domain decomposition and nonlinear elimination. Numerical results will be
presented to examine the performance of the newly developed algorithm on
parallel computers. It was observed from numerical tests that our nonlinear
solver overcomes the severe limits on the time step associated with conventional methods, and it results in superior convergence performance, often reducing the
total computing time by more than one order of magnitude. This presentation is
based on the joint work [1-7] with Haijian Yang (Hunan University), Chao Yang
(Beijing University), Yiteng Li (KAUST), Huangxin Chen (Xiamen University),
Jisheng Kou (Hubei Engineering University), Xiaolin Fan (KAUST), Tao Zhang
(KAUST).
KW -
DO - 10.32604/icces.2021.08590