Summary
This paper investigates the accuracy of first- and high-order numerical
methods in simulating enhanced condensate processes in 1D, 2D, and 3D. We
compare the predictions of a standard single point upwind (SPU) scheme with a
third-order accurate finite difference (FD) simulator based on a third-order
essentially nonoscillatory (ENO) flux reconstruction with matching temporal
accuracy. We include physical dispersion in the mathematical model of these
multiphase, multicomponent systems.
The comparisons demonstrate that SPU schemes may fail to predict the
formation of the mobile liquid bank at the leading edge of the displacement
unless an impractical number of gridblocks is used in the simulations. In
contrast, the high-order FD simulator is demonstrated to accurately predict the
liquid bank at much lower grid resolution, providing for a more efficient
simulation approach. In 2D displacement calculations with gravity included, the
CPU requirement of the SPU scheme was found to be more than 50 times larger
than for the ENO scheme for a given level of accuracy. In 2D vertical
cross-sections, the predicted component recovery is demonstrated to vary upward
of 8% depending on the selected numerical scheme for a given grid resolution
and dispersivity. In these settings, the SPU solutions converge to the ENO
results upon significant grid refinement.
In 3D displacement calculations, the magnitude of the predicted condensate
bank is also found to be very different depending on the selected numerical
scheme. Relative to the 2D displacement calculations, condensate banking and
gravity segregation is observed to have less impact on the process performance
prediction because of the permeability configuration in the 3D model used here,
but it could have a high impact in different settings.
We include an explicit representation of longitudinal and transverse
dispersion in the porous medium to demonstrate the grid resolution required to
resolve physical dispersion at a given simulation length scale, and to show
that condensate banks can also form in more realistic dispersive systems.
Grid-refinement studies in 1D and 2D demonstrate, again, that the ENO scheme
outperforms the SPU scheme for a given Peclet (Pe) number. Converged solutions
are obtained with the ENO scheme using a relatively small number of grid cells.
In addition, we show the behavior of the two schemes for varying Peclet numbers
on a fixed simulation grid. For this grid, the ENO scheme is shown to be
sensitive to the Peclet number, signifying that physical dispersion is not
overwhelmed by numerical diffusion. For the SPU scheme, however, the solutions
are almost independent of the Peclet number, which indicates that numerical
diffusion dominates.
Introduction
Significant portions of the current hydrocarbon reserves are found in
gas-condensate-carrying formations. Production of hydrocarbons from these
reserves is expected to increase upward of 100% by 2015 (Cambridge Energy
Research Associates 2005). Primary production of these reserves will result in
significant loss of the heavy ends because of liquid dropout once the reservoir
pressure reaches the dew point pressure. Enhanced condensate recovery by gas
cycling/injection schemes are often applied to extend the lifetime of
condensate reservoirs. These processes are inherently compositional, as the
component transfer between an immobile liquid phase and a mobile gas phase is
the key mechanism for enhancing recovery. Numerical simulation of such
processes is very challenging because the prediction of the local displacement
efficiency and the global sweep can be very sensitive to numerical diffusion.
Various authors have shown that numerical artifacts can alter the displacement
characteristics and lead to significant underprediction of the local
displacement efficiency (Stalkup et al. 1990; Lim et al. 1997; Johns et al.
2002; Jessen et al. 2004).
In their numerical studies of gas injection in depleted condensate
reservoirs, Høier and Whitson (2001) demonstrated that near-miscible gas
injection may, in some cases, lead to the formation of a condensate bank at the
leading edge of the displacement. In addition, for some injection settings, the
liquid bank was shown to exceed the critical liquid saturation and hence become
mobile. Their analysis was based on 1D displacement calculations.
The work of Jessen and Orr (2004) demonstrated that the prediction of
condensate banks that exceed the critical condensate saturation by numerical
calculations requires a firm control of numerical diffusion. They used
analytical solutions based on the method of characteristics (MOC) (Johns et al.
1993) as well as a high-resolution FD simulator developed by Mallison et al.
(2005) to investigate the complex interplay of flow and phase behavior in
enhanced condensate recovery processes in 1D. In this work, we extend this
investigation of enhanced condensate recovery processes to 2D and 3D. We
include gravity to study the impact of a mobile liquid bank on the overall
efficiency of the enhanced condensate recovery (ECR) process.
We investigate the grid resolutions needed for both numerical schemes to
resolve the condensate banks, and the impact of numerical errors on the
predicted recovery in the presence of gravity. We also study the importance of
physical dispersion in ECR processes. In particular, we are interested in
understanding the grid resolution that is required to resolve the physical
dispersion terms by controlling the level of numerical diffusion. We note that
physical dispersion/diffusion is required to obtain a converged solution in 2D
and 3D for this type of displacement problem.
In the following section, we introduce the mathematical model for
multicomponent multiphase flow in porous media, including an explicit
representation of dispersive terms. We then describe the implementation in our
compositional simulator. Next, we discuss the condensate system investigated in
this work and present simulation results for enhanced condensate recovery in
1D, 2D, and 3D. Finally, we draw conclusions from the presented material.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
19 February 2006
- Meeting paper published:
22 April 2006
- Revised manuscript received:
5 November 2007
- Manuscript approved:
8 November 2007
- Version of record:
25 June 2008
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