@Article{icces.2021.08590,
AUTHOR = {Shuyu Sun},
TITLE = {Fully Phase-Wise Conservative and Bound-Preserving Algorithms for  Multiphase Flow in Geological Formation},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {23},
YEAR = {2021},
NUMBER = {1},
PAGES = {24--25},
URL = {http://www.techscience.com/icces/v23n1/42047},
ISSN = {1933-2815},
ABSTRACT = {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 Newton–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).},
DOI = {10.32604/icces.2021.08590}
}