Reduced Variable Method for General-Purpose Compositional Reservoir Simulation

2010 ◽  
Author(s):  
Huanquan Pan ◽  
Hamdi A. Tchelepi
Keyword(s):  
Reservoir Simulation ◽  
General Purpose ◽  
Variable Method

Multidimensional Upwinding for Multiphase Transport in Porous Media

SPE Journal ◽  
2011 ◽  
Vol 16 (02) ◽  
pp. 263-272 ◽  
Author(s):  
J.. Kozdon ◽  
B.. Mallison ◽  
M.. Gerritsen ◽  
W.. Chen
Keyword(s):  
Oil Recovery ◽  
Reservoir Simulation ◽  
Heterogeneous Media ◽  
General Purpose ◽  
Real Field ◽  
Multiphase Transport ◽  
The Family ◽  
Grid Design ◽  
Grid Orientation ◽  
Highly Correlated

Summary Multidimensional transport for reservoir simulation is typically solved by applying 1D numerical methods in each spatial-coordinate direction. This approach is simple, but the disadvantage is that numerical errors become highly correlated with the underlying computational grid. In many real-field applications, this can result in strong sensitivity to grid design not only for the computed saturation/composition fields but also for critical integrated data such as breakthrough times. Therefore, to increase robustness of simulators, especially for adverse-mobility-ratio flows that arise in a variety of enhanced-oil-recovery (EOR) processes, it is of much interest to design truly multidimensional schemes for transport that remove, or at least strongly reduce, the sensitivity to grid design. We present a new upstream-biased truly multidimensional family of schemes for multiphase transport capable of handling countercurrent flow arising from gravity. The proposed family of schemes has four attractive properties: applicability within a variety of simulation formulations with varying levels of implicitness, extensibility to general grid topologies, compatibility with any finite-volume flow discretization, and provable stability (monotonicity) for multiphase transport. The family is sufficiently expressive to include several previously developed multidimensional schemes, such as the narrow scheme, in a manner appropriate for general-purpose reservoir simulation. A number of waterflooding problems in homogeneous and heterogeneous media demonstrate the robustness of the method as well as reduced transverse (cross-wind) diffusion and grid-orientation effects.

Finite Difference Simulation of Geologically Complex Reservoirs With Tensor Permeabilities

1998 ◽  
Vol 1 (06) ◽  
pp. 567-574 ◽  
Author(s):  
S.H. Lee ◽  
L.J. Durlofsky ◽  
M.F. Lough ◽  
W.H. Chen
Keyword(s):  
Finite Difference ◽  
Reservoir Simulation ◽  
Reservoir Characterization ◽  
Heterogeneous Systems ◽  
General Purpose ◽  
Flow Problems ◽  
Continuous Approach ◽  
Original Manuscript ◽  
Element Approach ◽  
Reservoir Description

This paper (SPE 52637) was revised for publication from paper SPE 38002, first presented at the 1997 SPE Reservoir Simulation Symposium, Dallas, 8-11 June. Original manuscript received for review 1 July 1997. Revised manuscript received 5 August 1998. Paper peer approved 3 September 1998. Summary The gridblock permeabilities used in reservoir simulation are commonly determined through the upscaling of a fine scale geostatistical reservoir description. Though it is well established that permeabilities computed in this manner are, in general, full tensor quantities, most finite difference reservoir simulators still treat permeability as a diagonal tensor. In this paper, we implement a capability to handle full tensor permeabilities in a general purpose finite difference simulator and apply this capability to the modeling of several complex geological systems. We formulate a flux continuous approach for the pressure equation by use of a method analogous to that of previous researchers (Edwards and Rogers; Aavatsmark et al.), consider methods for upwinding in multiphase flow problems, and additionally discuss some relevant implementation and reservoir characterization issues. The accuracy of the finite difference formulation, assessed through comparisons to an accurate finite element approach, is shown to be generally good, particularly for immiscible displacements in heterogeneous systems. The formulation is then applied to the simulation of upscaled descriptions of several geologically complex reservoirs involving crossbedding and extensive fracturing. The method performs quite well for these systems and is shown to capture the effects of the underlying geology accurately. Finally, the significant errors that can be incurred through inaccurate representation of the full permeability tensor are demonstrated for several cases. P. 567

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