25 research outputs found
A constrained pressure-temperature residual (CPTR) method for non-isothermal multiphase flow in porous media
For both isothermal and thermal petroleum reservoir simulation, the
Constrained Pressure Residual (CPR) method is the industry-standard
preconditioner. This method is a two-stage process involving the solution of a
restricted pressure system. While initially designed for the isothermal case,
CPR is also the standard for thermal cases. However, its treatment of the
energy conservation equation does not incorporate heat diffusion, which is
often dominant in thermal cases. In this paper, we present an extension of CPR:
the Constrained Pressure-Temperature Residual (CPTR) method, where a restricted
pressure-temperature system is solved in the first stage. In previous work, we
introduced a block preconditioner with an efficient Schur complement
approximation for a pressure-temperature system. Here, we extend this method
for multiphase flow as the first stage of CPTR. The algorithmic performance of
different two-stage preconditioners is evaluated for reservoir simulation test
cases.Comment: 28 pages, 2 figures. Sources/sinks description in arXiv:1902.0009
A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based flow simulations
In this work we propose a novel block preconditioner, labelled Explicit
Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov
subspace solvers used to address the sequence of non-symmetric systems of
linear equations originating from flow simulations in porous media. The flow
model is discretized blending the Mixed Hybrid Finite Element (MHFE) method for
Darcy's equation with the Finite Volume (FV) scheme for the mass conservation.
The EDFA preconditioner is characterized by two features: the exploitation of
the system matrix decoupling factors to recast the Schur complement and their
inexact fully-parallel computation by means of restriction operators. We
introduce two adaptive techniques aimed at building the restriction operators
according to the properties of the system at hand. The proposed block
preconditioner has been tested through an extensive experimentation on both
synthetic and real-case applications, pointing out its robustness and
computational efficiency